index int64 0 999 | image stringlengths 4.4k 871k | question stringlengths 189 2.04k | answer stringclasses 4
values | category stringclasses 6
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values | reasoning_type stringclasses 20
values | embedding listlengths 4.1k 4.1k |
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200 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE+AcYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A spider of mass \(0.30\,\mathrm{g}\) waits in its web of negligible mass. A slight movement causes the web to vibrate with a frequency of about \(15\,\mathrm{Hz}\).An insect of mass \(0.10\,\mathrm{g}\) were trapped in addition to the spider. At what frequency would you expect the web to vibrate?Please directly answer... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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201 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJQAb4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The animal emits a pulse of sound which, after reflection from objects, returns and is detected by the animal. Echolocation waves can have frequencies of about 100{,}000\,\mathrm{Hz}.An obstacle is 100\,\mathrm{m} from the animal. How long after the animal emits a wave is its reflection detected?Please directly answer ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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202 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFwAmwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | She fires a bullet into a 4.148\,\mathrm{kg} wooden block resting on a smooth surface, and attached to a spring of spring constant \( k = 162.7\,\mathrm{N/m} \). The bullet, whose mass is 7.870\,\mathrm{g}, remains embedded in the wooden block. What is the speed \( v \) of the bullet?Please directly answer the question... | D | Waves/Acoustics | Momentum and Collisions | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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203 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEaANADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block is supported by two identical parallel vertical springs, each with spring stiffness constant \( k \). What will be the frequency of vertical oscillation?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $\frac{1}{2\pi} \sqrt{\frac{k}{2m}}$ B: $\frac{1}{... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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204 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKAwIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | One end of a horizontal string is attached to a small-amplitude mechanical 60.0\,\mathrm{Hz} oscillator. The string's mass per unit length is \( 3.5 \times 10^{-4}\,\mathrm{kg/m} \).Assume the string at the oscillator is a node, which is nearly true. What mass \( m \) must be hung from this end of the string to produce... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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205 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADyAkADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A diving board oscillates with simple harmonic motion of frequency \( 2.8 \) cycles per second. The end of the board must oscillate with an amplitude small enough that a pebble placed there does not lose contact with it during the motion. What is the maximum amplitude?Please directly answer the question and provide the... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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206 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGoAgYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You walk with a cup of coffee (diameter \( 8\,\mathrm{cm} \)) at just the right pace of about one step per second. Estimate the speed of the waves in the coffee.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 8cm/s B: 12cm/s C: 16cm/s D: 20cm/s | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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207 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADuAkQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Carbon dioxide is a linear molecule. The carbon--oxygen bonds in this molecule act very much like springs.Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs at a frequency \( f = 2.83 \times 10^{13}\,\mathrm{Hz} \). ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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208 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4AiADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A string can have a free end if that end is attached to a ring that can slide without friction on a vertical pole. Dtermine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. ... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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209 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFmAhQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | For any type of wave that reaches a boundary beyond which its speed is increased, there is a maximum incident angle if there is to be a transmitted refracted wave. This maximum incident angle \( \theta_{i\mathrm{M}} \) corresponds to an angle of refraction equal to \( 90^{\circ} \). If \( \theta_i > \theta_{i\mathrm{M}... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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210 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIaApYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A highway overpass was observed to resonate as one full loop \( \left( \frac{1}{2}\lambda \right) \) when a small earthquake shook the ground vertically at \( 3.0\,\mathrm{Hz} \). What resonant frequency would you now expect for the overpass?Please directly answer the question and provide the correct OPTION LETTER ONL... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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211 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAESApADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Autofocusing cameras emit a pulse of very high frequency sound that travels to the object being photographed, and include a sensor that detects the returning reflected sound. Calculate the travel time of the pulse for an object \( 20\,\mathrm{m} \) away.Please directly answer the question and provide the correct OPTION... | D | Waves/Acoustics | Sound | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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212 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI6AiIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The sound level measured \( 30\,\mathrm{m} \) from a jet plane is \( 140\,\mathrm{dB} \).(Ignore reflections from the ground.) Estimate the sound level at \( 300\,\mathrm{m} \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 160dB B: 140dB C: 100dB D: 120dB | D | Waves/Acoustics | Sound | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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213 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHSAeIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Wind can be noisy—it can \"howl\" in trees; it can \"moan\" in chimneys. What is the sound frequency of the vibrating tree branch?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 440Hz B: 460Hz C: 480Hz D: 500Hz | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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214 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEAAgIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A \( 5000\,\mathrm{Hz} \) sound wave is emitted by a stationary source. This sound wave reflects from an object moving toward the source. What is the frequency of the wave reflected by the moving object as detected by a detector at rest near the source?Please directly answer the question and provide the correct OPTION ... | D | Waves/Acoustics | Sound | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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215 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHEAqgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An ocean fishing boat is drifting just above a school of tuna on a foggy day.Without warning, an engine backfire occurs on another boat. How much time elapses before the backfire is heard by the fishermen?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3.52s ... | D | Waves/Acoustics | Sound | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.03125,
0.0069580078125,
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0.021484375,
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0.01275634765625,
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0.... |
216 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFoApYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A fireworks shell explodes above the ground, creating colorful sparks. The sound of the explosion for a person directly beneath the blast is compared to that for a person located away horizontally. How much greater is the sound level?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., ... | D | Waves/Acoustics | Sound | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.028564453125,
0.00077056884765625,
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217 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF2Ad4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You put your ear very near a \( 15\,\mathrm{cm} \)-diameter seashell. Estimate the frequency of the sound of the ocean.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 510Hz B: 530Hz C: 550Hz D: 570Hz | D | Waves/Acoustics | Sound | [] | [
0.01495361328125,
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0.0079345703125,
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218 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFSAkgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The string's tension and mass per unit length remain unchanged.If each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is \( 2^{1/12} \). Determine the positions \( x \) of the first fre... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.02001953125,
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219 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIqAgIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | They emit \( 474\,\mathrm{Hz} \) sounds, in phase. A microphone is placed between the two speakers, where an intensity maximum is recorded. How far must the microphone be moved to the right to find the first intensity minimum?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C,... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0252685546875,
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220 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAnoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You look directly overhead and see a plane exactly \( 1.45\,\mathrm{km} \) above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of \( 2.0\,\mathrm{km} \). Determine the angle of the shock cone, \( \theta \).Please directly answer the q... | D | Waves/Acoustics | Wave Properties | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01470947265625,
0.0155029296875,
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221 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEKAmwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A supersonic jet traveling at Mach \( 2.0 \) passes directly over an observer on the ground. Where will the plane be relative to the observer when the latter hears the sonic boom?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 28km B: 24km C: 20km D: 16km | D | Waves/Acoustics | Sound | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0164794921875,
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222 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4AqIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The speakers have identical sound frequencies of \( 348\,\mathrm{Hz} \).He is between the speakers, at B. What is the beat frequency heard by the observer?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 30Hz B: 18Hz C: 12Hz D: 24Hz | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.058349609375,
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0.00168609619140625,
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0.00170135498... |
223 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJWAeIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is \( 0.125\,\mathrm{m} \) and again at \( 0.395\,\mathrm{m} \). What is the frequency of the tuning fork?Please direct... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.017333984375,
0.0198974609375,
0.0118408203125,
0.00909423828125,
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0.002166748046875,
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0.00439453125,
0.0052490234375,
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0.01904296875,
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224 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALKAxgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The most popular alpenhorn is about \( 3.4\,\mathrm{m} \) long, and it is called the F\# (or G\flat) horn.Model as a tube open at both ends. What is the fundamental frequency of this horn?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 62Hz B: 56Hz C: 44Hz D:... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.032958984375,
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0.002166748046875,
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225 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD2AMADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | While driving behind a car traveling at \( 3.00\,\mathrm{m/s} \), you notice one of the car's tires. The radii of the car's tires are \( 0.300\,\mathrm{m} \). What is the bump's period of oscillation?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.928s B: 0... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0150146484375,
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0.01409912109375,
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0.0299072265625,
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0.035400390625,
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226 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC0AdwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A \( 0.250\,\mathrm{kg} \) block resting on a frictionless, horizontal surface is attached to a spring whose force constant is \( 83.8\,\mathrm{N/m} \) as in figure. A horizontal force \( \vec{F} \) causes the spring to stretch a distance of \( 5.46\,\mathrm{cm} \) from its equilibrium position. What is the total energ... | D | Waves/Acoustics | Work and Energy | ['Physical Model Grounding Reasoning'] | [
0.029052734375,
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227 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGsATYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A very light rigid rod extends straight out from one end of a meterstick. The combination is then pulled out by a small angle and released. By what percentage does the period differ from the period of a simple pendulum \( 1.00\,\mathrm{m} \) long?Please directly answer the question and provide the correct OPTION LETTER... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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228 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIqAfwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A wheel has a period of oscillation of \( 0.250\,\mathrm{s} \). The wheel is constructed so that its mass of \( 20.0\,\mathrm{g} \) is concentrated around a rim of radius \( 0.500\,\mathrm{cm} \). What is the torsion constant of the attached spring?Please directly answer the question and provide the correct OPTION LETT... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.013427734375,
0.00958251953125,
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0.001373291015625,
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0.00787353515625,
... |
229 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGWATQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A small ball is attached to the end of a uniform rod of equal mass \( M \) that is pivoted at the top.\( L = 2.00\,\mathrm{m} \). Determine this period.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 5.68s B: 4.68s C: 3.68s D: 2.68s | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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0.01220703125,
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230 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUAjoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An object attached to a spring vibrates with simple harmonic motion as described by Figure. For this motion, find the maximum acceleration.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $4.39\,\mathrm{cm/s^2}$ B: $5.93\,\mathrm{cm/s^2}$ C: $3.93\,\mathrm{cm/... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.03515625,
0.0084228515625,
-0.02734375,
-0.0048828125,
0.0115966796875,
-0.0017852783203125,
0.0032196044921875,
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0.0299072265625,
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0.001129150390625,
0.0130615234375,
0.01055908203125,
-0.040527... |
231 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADSAZQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A large block \( P \) attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency \( f = 1.50\,\mathrm{Hz} \).The coefficient of static friction between the two is \( \mu_s = 0.600 \).The block \( B \) is not to slip. What maximum amplitude of oscil... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
0.0247802734375,
0.0015106201171875,
-0.003143310546875,
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0.004486083984375,
0.0166015625,
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0.000537872314453125,
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0.0294189453125,
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0.003936767578125,
0.002197265625,
0.01049804687... |
232 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEoAbIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A horizontal plank of mass \( 5.00\,\mathrm{kg} \) and length \( 2.00\,\mathrm{m} \) is pivoted at one end. The plank's other end is supported by a spring of force constant \( 100\,\mathrm{N/m} \).The plank is displaced by a small angle from its horizontal equilibrium position and released.The plank moves with simple h... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.01611328125,
-0.000858306884765625,
-0.0023651123046875,
0.022216796875,
0.00093841552734375,
0.03125,
-0.0260009765625,
-0.01300048828125,
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0.0147705078125,
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0.01806640625,
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0.00665283203125,
0.01239013671875,
0.005523681640625,
... |
233 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGqASIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A pendulum has a spring of force constant connected to it at a distance below its point of suspension. Assume the vertical suspension rod of length \( L \) is rigid, but ignore its mass. Find the frequency of vibration of the system for small values of the amplitude (small \( \theta \)).Please directly answer the quest... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.006134033203125,
-0.0167236328125,
0.00787353515625,
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0.009521484375,
0.030029296875,
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0.00872802734375,
-0.0106201171875,
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0.01324462890625,
0.01007080078125,
0.0130004882812... |
234 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC6AfwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light balloon filled with helium of density \( 0.179\,\mathrm{kg/m^3} \) is tied to a light string of length \( L = 3.00\,\mathrm{m} \).The balloon is displaced slightly from equilibrium and released.Take the density of air to be \( 1.20\,\mathrm{kg/m^3} \).Assume the air applies a buoyant force on the balloon but do... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01324462890625,
-0.017333984375,
0.007110595703125,
-0.0009002685546875,
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0.031005859375,
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-0.01007080078125,
-0.002532958984375,
0.033203125,
-0.01513671875,
0.033935546875,
0.000732421875,
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0.01129150390625,
0.0011825561523437... |
235 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEcAZwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | One end of a light spring with force constant \( k = 100\,\mathrm{N/m} \) is attached to a vertical wall. A light string is tied to the other end of the horizontal spring.The string changes from horizontal to vertical as it passes over a pulley in the shape of a solid disk of radius \( R = 2.00\,\mathrm{cm} \). The pul... | D | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.00823974609375,
0.0098876953125,
0.00775146484375,
0.0133056640625,
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0.04833984375,
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0.0172119140625,
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0.01470947265625,
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0.01153564453125,
0.0133056640625,
0.0091552734375,
-0.023... |
236 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALAAjoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An object of mass \( m_1 = 9.00\,\mathrm{kg} \) is in equilibrium when connected to a light spring of constant \( k = 100\,\mathrm{N/m} \) that is fastened to a wall. A second object, \( m_2 = 7.00\,\mathrm{kg} \), is slowly pushed up against \( m_1 \), compressing the spring by the amount \( A = 0.200\,\mathrm{m} \). ... | D | Waves/Acoustics | Wave Properties | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0244140625,
0.01116943359375,
-0.01434326171875,
-0.0164794921875,
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0.006072998046875,
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0.005828857421875,
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0.03271484375,
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0.0179443359375,
0.003936767578125,
... |
237 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADKAkADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block of mass \( M \) is connected to a spring of mass \( m \) and oscillates in simple harmonic motion on a frictionless, horizontal track.The force constant of the spring is \( k \), and the equilibrium length is \( \ell \). Assume all portions of the spring oscillate in phase and the velocity of a segment of the s... | D | Waves/Acoustics | Wave Properties | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0235595703125,
-0.0184326171875,
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0.0103759765625,
0.00347900390625,
0.0155029296875,
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0.0157470703125,
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0.0064697265625,
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0.000514984130859375,
0.006439208984375,
... |
238 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFOAcQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light, cubical container is initially filled with a liquid of mass density \( \rho \).The cube is initially supported by a light string to form a simple pendulum, measured from the center of mass of the filled container, where \( L_i \gg a \). The liquid is allowed to flow from the bottom of the container at a consta... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00653076171875,
0.004364013671875,
-0.003875732421875,
-0.00543212890625,
0.01397705078125,
0.0133056640625,
0.0045166015625,
-0.021240234375,
-0.00775146484375,
-0.005706787109375,
-0.0152587890625,
-0.01080322265625,
-0.0225830078125,
-0.0286865234375,
0.003936767578125,
0.00328063... |
239 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF4AXADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Assume the waves move in straight lines through uniform material. The S waves travel through the Earth more slowly than the P waves (at about \( 5\,\mathrm{km/s} \) versus \( 8\,\mathrm{km/s} \)). How many detection stations are necessary to locate the focus unambiguously?Please directly answer the question and provide... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0264892578125,
0.006103515625,
-0.03271484375,
0.0196533203125,
-0.004364013671875,
0.0033721923828125,
0.002227783203125,
-0.0025177001953125,
-0.03955078125,
0.0021820068359375,
-0.0208740234375,
-0.0019378662109375,
-0.03271484375,
-0.02099609375,
-0.00106048583984375,
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240 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACYAhgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The string is driven at a frequency of \( 5.00\,\mathrm{Hz} \). The amplitude of the motion is \( A = 12.0\,\mathrm{cm} \), and the wave speed is \( v = 20.0\,\mathrm{m/s} \). Furthermore, the wave is such that \( y = 0 \) at \( x = 0 \) and \( t = 0 \). Determine the maximum transverse acceleration of an element of th... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.05419921875,
0.0218505859375,
-0.000637054443359375,
-0.010986328125,
-0.009521484375,
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-0.0247802734375,
0.0257568359375,
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0.0159912109375,
0.0289306640625,
0.020874023... |
241 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4AUwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Tension is maintained in a string. The observed wave speed is \( v = 24.0\,\mathrm{m/s} \) when the suspended mass is \( m = 3.00\,\mathrm{kg} \).The suspended mass is \( m = 2.00\,\mathrm{kg} \). What is the wave speed?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OP... | D | Waves/Acoustics | Wave Properties | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.00872802734375,
0.010498046875,
-0.0064697265625,
0.0013427734375,
0.00469970703125,
0.0152587890625,
-0.013427734375,
-0.00173187255859375,
-0.03076171875,
0.021484375,
-0.038818359375,
0.0272216796875,
0.00018978118896484375,
0.00738525390625,
0.031005859375,
0.025634765625,
-0.0... |
242 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFaAbADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light string with a mass per unit length of \( 8.00\,\mathrm{g/m} \) has its ends tied to two walls separated by a distance. An object is suspended from the center of the string, putting a tension in the string.The wave speed is to be \( 60.0\,\mathrm{m/s} \). What should be the mass of the object suspended from the ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0169677734375,
-0.003753662109375,
0.0054931640625,
-0.0264892578125,
0.00087738037109375,
0.035888671875,
0.01190185546875,
-0.007110595703125,
-0.01019287109375,
-0.0289306640625,
-0.04345703125,
0.01336669921875,
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0.00213623046875,
0.034423828125,
0.00946044921875,... |
243 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGGArADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block of mass \( M = 0.450\,\mathrm{kg} \) is attached to one end of a cord of mass \( 0.003\,20\,\mathrm{kg} \); the other end of the cord is attached to a fixed point. The block rotates with constant angular speed in a circle on a frictionless, horizontal table. Through what angle does the block rotate in the time ... | D | Waves/Acoustics | Wave Properties | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0250244140625,
0.0052490234375,
0.0028076171875,
-0.0294189453125,
-0.0172119140625,
0.0203857421875,
-0.0031280517578125,
-0.01513671875,
-0.03564453125,
0.0137939453125,
-0.0184326171875,
0.042236328125,
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0.0002307891845703125,
0.026611328125,
0.0162353515625,
-0... |
244 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD6AgADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without collapsing. Consider a chain of uniform linear mass density \( \mu \) whose center of mass travels to the right.Assume the weight of an individual link is negligible compared to the tension. Determine the tension in the ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.017578125,
-0.006622314453125,
-0.006805419921875,
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0.0096435546875,
0.00506591796875,
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0.00909423828125,
-0.0172119140625,
0.000911712646484375,
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0.007080078125,
0.00738525390625,
0.013916015625,
-0.0281982... |
245 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADGAioDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Helium-neon lasers commonly used in classroom demonstrations and supermarket checkout scanners. A helium-neon laser operates at a wavelength of precisely $632.9924 \, \mathrm{nm}$ when the spacing between the mirrors is $310.372 \, \mathrm{mm}$. What is the next longest wavelength that could form a standing wave in thi... | A | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0142822265625,
0.00439453125,
-0.03857421875,
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0.0037841796875,
0.0019378662109375,
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246 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJqAngDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two loudspeakers in a plane. They emit equal-amplitude sound waves. Each speaker alone creates sound with intensity $I_0$. An observer at point $A$ in front of the plane containing the two loudspeakers and centered between them. A second observer at point $B$ directly in front of one of the speakers. In terms of $I_0$,... | A | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01708984375,
0.003814697265625,
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247 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJCA0QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Your firm has been hired to design a system that allows airplane pilots to make instrument landings in rain or fog. These two transmitters will broadcast the same frequency, but out of phase with each other. This will cause a nodal line to extend straight off the end of the runway. As long as the airplane's receiver is... | A | Waves/Acoustics | Wave Properties | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.04833984375,
0.01904296875,
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-0.029052734375,
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248 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALgA5oDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Light from a helium-neon laser ($\lambda = 633\;nm$) illuminates two slits spaced $0.40\;mm$ apart. A viewing screen is $2.0\;m$ behind the slits. What is the distance between the two $m = 2$ dark fringes?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 15.8mm... | A | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0274658203125,
0.00732421875,
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-0.01300048828125,
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249 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJSAnQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Light from a helium-neon laser ($\lambda = 633\;nm$) passes through a narrow slit and is seen on a screen $2.0\;m$ behind the slit. The first minimum in the diffraction pattern is $1.2\;cm$ from the central maximum. How wide is the slit?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g... | A | Waves/Acoustics | Wave Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.028076171875,
0.00182342529296875,
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0.000743865966796875,
0.0177001953125,
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250 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIMAoYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A Michelson interferometer uses a helium-neon laser with wavelength $\lambda_{vac} = 633\;nm$. In one arm, the light passes through a $4.00\;cm$-thick glass cell. Initially the cell is evacuated, and the interferometer is adjusted so that the central spot is a bright fringe. The cell is then slowly filled to atmospheri... | A | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.022705078125,
0.006317138671875,
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0.039306640625,
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0.009521484375,
0.020263671875,
0.006988525390625,
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251 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGIAeQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The vertical axis scale is set by $x_s = 6.0\ cm$. What is the phase constant (positve) for the harmonic oscillator with the position function $x(t)$ given in figure if the position function has the form $x = x_m \cos(\omega t + \phi)$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00482177734375,
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0.00762939453125,
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252 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADMAjwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure, and the floor is frictionless. If the left spring is removed, the block oscillates at a frequency of $30\ Hz$. If, instead, the spring on the right is removed, the block oscillates at a frequency of $45\ Hz$. At what frequency does the block oscillate with both springs attached?Please directly answe... | C | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.04931640625,
0.01434326171875,
0.0164794921875,
0.0072021484375,
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0,
0.0078125,
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0.0172119140... |
253 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFuAiQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The vertical axis scale is set by $v_s = 4.0\ cm/s$. What is the phase constant (positive) for the harmonic oscillator with the velocity function $v(t)$ given in figure if the position function $x(t)$ has the form $x = x_m \cos(\omega t + \phi)$?Please directly answer the question and provide the correct OPTION LETTER ... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0162353515625,
0.00107574462890625,
0.00787353515625,
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0.004547119140625,
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0.0242919921875,
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0.043212890625,
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0.02685546875,
0.01867675781... |
254 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMcAdIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure a is a partial graph of the position function $x(t)$ for a simple harmonic oscillator with an angular frequency of $1.20\ rad/s$; Figure b is a partial graph of the corresponding velocity function $v(t)$. The vertical axis scales are set by $x_s = 5.0\ cm$ and $v_s = 5.0\ cm/s$. What is the phase constant (posit... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0269775390625,
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0.01092529296875,
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0.04052734375,
0.0098876953125,
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255 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEAAg4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows block 1 of mass $0.200\ kg$ sliding over a frictionless elevated surface at a speed of $8.00\ m/s$. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant $1208.5\ N/m$. (Assume that the spring does not affect the collision.) After the collision, ... | C | Waves/Acoustics | Wave Properties | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03369140625,
-0.027587890625,
-0.01361083984375,
0.01019287109375,
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0.003631591796875,
0.00131988525390625,
0.0152587890625,
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0.0205078125,
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0.027587890625,
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256 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACeAaIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, two springs are joined and connected to a block of mass $0.245\ kg$ that is set oscillating over a frictionless floor. The springs each have spring constant $k = 6430\ N/m$. What is the frequency of the oscillations?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.03662109375,
0.021484375,
0.00506591796875,
0.010009765625,
0.0020751953125,
0.0208740234375,
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0.00799560546875,
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0.02783203125,
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0.0142822265625,
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257 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFeAX4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a block weighing $14.0\ N$, which can slide without friction on an incline at angle $\theta = 40.0^\circ$, is connected by a massless spring of unstretched length $0.450\ m$ and spring constant $120\ N/m$. If the block is pulled slightly down the incline and released, what is the period of the resulting osci... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.004364013671875,
-0.0135498046875,
-0.000698089599609375,
0.00665283203125,
0.004241943359375,
0.015380859375,
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0.0177001953125,
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0.00946044921875,
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258 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADKAbYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, two blocks ($m = 1.8\ kg$ and $M = 10\ kg$) and a spring ($k = 200\ N/m$) are arranged on a horizontal, frictionless surface. The coefficient of static friction between the two blocks is $0.40$. What amplitude of simple harmonic motion of the spring$-$blocks system puts the smaller block on the verge of slip... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
0.0220947265625,
-0.0048828125,
0.01422119140625,
-0.0181884765625,
0.000736236572265625,
0.033203125,
0.00885009765625,
0.010986328125,
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0.00665283203125,
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0.01153564453125,
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0.02099609375,
0.001312255859375,
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259 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF6AdIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the kinetic energy $K$ of a simple harmonic oscillator versus its position $x$. The vertical axis scale is set by $K_s = 4.0\ J$. What is the spring constant?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $7.9 \times 10^2\\ N/m$ B: $8.0 \times 1... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.034423828125,
0.00775146484375,
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0.0047607421875,
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0.0128173828125,
0.016845703125,
0.0123291015625,
-0.03906... |
260 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC2AZoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a block of mass $M = 5.4\ kg$, at rest on a frictionless table, is attached to a rigid support by a spring of constant $k = 6000\ N/m$. A bullet of mass $m = 9.5\ g$ and velocity $\vec{v}$ of magnitude $630\ m/s$ strikes and is embedded in the block. Assuming the compression of the spring is negligible until... | C | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.037353515625,
0.00168609619140625,
-0.01708984375,
0.0032958984375,
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0.0257568359375,
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0.01611328125,
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0.0098876953125,
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0.0322265625,
-0.009765625,
0.00665283203125,
0.03466796875,
0.00958251953125,
-0.03125,
0.043701... |
261 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACAAagDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, block 2 of mass $2.0\ kg$ oscillates on the end of a spring in SHM with a period of $20\ ms$. The block's position is given by $x = (1.0\ cm) \cos(\omega t + \pi/2)$. Block 1 of mass $4.0\ kg$ slides toward block 2 with a velocity of magnitude $6.0\ m/s$, directed along the spring's length. The two blocks un... | C | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.028076171875,
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-0.005584716796875,
0.003753662109375,
0.0093994140625,
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0.0096435546875,
0.02734375,
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0.... |
262 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHSAZ4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, the pendulum consists of a uniform disk with radius $r = 10.0\ cm$ and mass $500\ g$ attached to a uniform rod with length $L = 500\ mm$ and mass $270\ g$. Calculate the period of oscillation.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.0 s B:... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01287841796875,
0.00244140625,
-0.005767822265625,
0.011474609375,
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0.0242919921875,
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0.0250244140625,
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0.04052734375,
0.000843048095703125,
-0.0150146484375,
0.038818359375,
0.001251220703125,
-0... |
263 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADUAMoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A physical pendulum consists of two $1\ m$-long sticks joined together as shown in figure. What is the pendulum's period of oscillation about a pin inserted through point $A$ at the center of the horizontal stick?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0198974609375,
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0.020263671875,
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0.0322265625,
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-0.022216796875,
0.014404296875,
-0.0203857421875,
0.04638671875,
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0.037109375,
0.004058837890625,
-0.03125,... |
264 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4ARgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a physical pendulum consists of a uniform solid disk (of radius $R = 2.35\ cm$) supported in a vertical plane by a pivot located a distance $d = 1.75\ cm$ from the center of the disk. The disk is displaced by a small angle and released. What is the period of the resulting simple harmonic motion?Please direct... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0048828125,
0.009033203125,
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0.0201416015625,
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0.0283203125,
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0.0272216796875,
0.0093994140625,
-0.040... |
265 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI+AhQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rectangular block, with face lengths $a = 35\ cm$ and $b = 45\ cm$, is to be suspended on a thin horizontal rod running through a narrow hole in the block. The block is then to be set swinging about the rod like a pendulum, through small angles so that it is in SHM. Figure shows one possible position of the hole, at ... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0257568359375,
-0.011474609375,
0.005615234375,
-0.021484375,
0.0031890869140625,
0.0264892578125,
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0.03125,
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0.03076171875,
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0.030029296875,
0.005767822265625,
-0.0223388671875,
... |
266 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJYAhoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a stick of length $L = 1.85\ m$ oscillates as a physical pendulum. What is that least period?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4 s B: 1.8 s C: 2.1 s D: 2.4 s | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.008056640625,
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0.01324462890625,
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0.01263427734375,
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0.021240234375,
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0.0230712890625,
-0.0140380859375,
-0.01141357421875,
0.041748046875,
-0.004669189453... |
267 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFKARQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The $3.00\ kg$ cube in figure has edge lengths $d = 6.00\ cm$ and is mounted on an axle through its center. A spring ($k = 1200\ N/m$) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated $3^\circ$ and released, what is the period of the resulting SHM?Plea... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0220947265625,
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0.0030517578125,
0.006927490234375,
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0.0198974609375,
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-0.0024566650390625,
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0.02587890625,
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0.0274658203125,
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0.0162353515625,
0.033935546875,
0.00555419921875,
-0.0172119140... |
268 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEKAiYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In the overhead view of figure, a long uniform rod of mass $0.600\ kg$ is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant $k = 1850\ N/m$ is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to t... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.021728515625,
-0.0028076171875,
0.01202392578125,
0.00634765625,
-0.010009765625,
0.041748046875,
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0.023193359375,
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0.041748046875,
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0.0286865234375,
0.0130615234375,
-0.0187... |
269 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAISBIIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a metal plate is mounted on an axle through its center of mass. A spring with $k = 2000\ N/m$ connects a wall with a point on the rim a distance $r = 2.5\ cm$ from the center of mass. Initially the spring is at its rest length. If the plate is rotated by $7^\circ$ and released, it rotates about the axle in S... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.025390625,
-0.00408935546875,
0.00640869140625,
0.01116943359375,
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0.0537109375,
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0.03125,
0.0022735595703125,
0.0322265625,
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0.000396728515625,
0.0291748046875,
-0.0089111328125,
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0.02... |
270 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKkAhQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a $2.50\ kg$ disk of diameter $D = 42.0\ cm$ is supported by a rod of length $L = 76.0\ cm$ and negligible mass that is pivoted at its end. What is the torsion constant of the spring if the period of oscillation has been decreased by $0.500\ s$?Please directly answer the question and provide the correct OPTI... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01373291015625,
0.007110595703125,
-0.01080322265625,
-0.01287841796875,
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0.045654296875,
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-0.01202392578125,
-0.030517578125,
0.01373291015625,
-0.0186767578125,
0.0322265625,
0.0216064453125,
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0.0220947265625,
0.0030364990234... |
271 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHeAaYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, three $10000\ kg$ ore cars are held at rest on a mine railway using a cable, which are inclined at angle $\theta = 30^\circ$. The cable stretches $15\ cm$ just before the coupling between the two lower cars breaks, detaching the lowest car. Assuming that the cable obeys Hooke's law, find the amplitude of the... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0296630859375,
-0.00634765625,
0.012451171875,
-0.0167236328125,
-0.0108642578125,
0.015380859375,
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0.030517578125,
-0.033447265625,
-0.02001953125,
-0.041748046875,
0.01483154296875,
-0.00176239013671875,
0.01483154296875,
0.0159912109375,
0.016845703125,
-0.0249... |
272 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFiAeADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A wheel is free to rotate about its fixed axle. Assuming that the wheel is a hoop of mass $m$ and radius $R$, What is $\omega$ if $r = R$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $\sqrt{k/2m}. $ B: $\sqrt{2k/m}. $ C: $\sqrt{k/m}. $ D: 0 | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.006072998046875,
-0.00994873046875,
-0.0086669921875,
0.03076171875,
-0.0001316070556640625,
0.0186767578125,
-0.0218505859375,
-0.01116943359375,
-0.03271484375,
0.0133056640625,
-0.0076904296875,
0.0208740234375,
-0.034423828125,
0.0211181640625,
0.0079345703125,
-0.000740051269531... |
273 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAH+A/wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives the position $x(t)$ of a block oscillating in SHM on the end of a spring ($t_s = 40.0\ ms$). What is the magnitude of the radial acceleration of a particle in the corresponding uniform circular motion?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: ... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0322265625,
0.004638671875,
0.00775146484375,
0.01300048828125,
-0.022216796875,
0.0247802734375,
0.0003643035888671875,
-0.0030517578125,
-0.021728515625,
0.017578125,
-0.0228271484375,
0.03857421875,
-0.023681640625,
0.0133056640625,
0.033203125,
0.005645751953125,
-0.04052734375... |
274 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGCAcwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the kinetic energy $K$ of a simple pendulum versus its angle $\theta$ from the vertical. The vertical axis scale is set by $K_s = 10.0\ mJ$. The pendulum bob has mass $0.200\ kg$. What is the length of the pendulum?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, ... | C | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01495361328125,
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0.02099609375,
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0.0162353515625,
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0.01373291015625,
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0.040771484375,
-0.0034027099609375,
-0.00885009765625,
0.0247802734375,
0.0140380859375,
-0.0... |
275 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFcAggDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A simple harmonic oscillator consists of a $0.50\ kg$ block attached to a spring. The block slides back and forth along a straight line on a frictionless surface with equilibrium point $x = 0$. At $t = 0$ the block is at $x = 0$ and moving in the positive $x$ direction. A graph of the magnitude of the net force $\vec{F... | C | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0286865234375,
0.00579833984375,
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0.0081787109375,
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0.0125732421875,
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276 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJuAdYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A grandfather clock has a pendulum that consists of a thin brass disk of radius $r = 15.00$ cm and mass $1.000$ kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in figure. If the pendul... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00775146484375,
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277 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGUAcoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure. What is the phase constant (positive) for SMH with $a(t)$ given in figure if the position function $x(t)$ has the form $x = x_m \cos(\omega t + \phi)$ and $a_s = 4.0$ m/s$^2$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.48 rad B: 1.65... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.003936767578125,
0.00848388671875,
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0.0101318359375,
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278 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJSAl4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure gives the magnitude $\tau$ of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle $\theta$. The... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.01513671875,
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0.00897216796875,
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279 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADGAdIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a solid cylinder attached to a spring ($k = 3.00$ N/m) rolls without slipping along a surface. If the system is released from rest when the spring is stretched by $0.250$ m, find the rotational kinetic energy of the cylinder as it passes through the equilibrium position.Please directly answer the question an... | D | Waves/Acoustics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00653076171875,
0.01068115234375,
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0.002044677734375,
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280 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGAAqgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A simple harmonic oscillator consists of a block attached to a spring with \(k = 200\,\mathrm{N/m}\). The block slides on a frictionless surface, with equilibrium point \(x = 0\) and amplitude \(0.20\,\mathrm{m}\). A graph of the block's velocity \(v\) as a function of time \(t\) is shown in figure. The horizontal scal... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0213623046875,
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0.006561279296875,
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281 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEaAcADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows that if we hang a block on the end of a spring with spring constant $k$, the spring is stretched by distance $h = 2.0$ cm. If we pull down on the block a short distance and then release it, it oscillates vertically with a certain frequency. What length must a simple pendulum have to swing with that frequen... | D | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0179443359375,
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0.0009765625,
0.00775146484375,
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0.0052490234375,
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0.022705078125,
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282 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALMAZgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The physical pendulum in figure has two possible pivot points $A$ and $B$. Point $A$ has a fixed position but $B$ is adjustable along the length of the pendulum as indicated by the scaling. When suspended from $A$, the pendulum has a period of $T = 1.80$ s. The pendulum is then suspended from $B$, which is moved until ... | D | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0277099609375,
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0.0031280517578125,
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283 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAICAV4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A common device for entertaining a toddler is a jump seat that hangs from the horizontal portion of a doorframe via elastic cords. Assume that only one cord is on each side in spite of the more realistic arrangement shown. When a child is placed in the seat, they both descend by a distance $d_s$ as the cords stretch (t... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0263671875,
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-0.0101318359375,
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0.01055908203125,
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0.007293701171875,
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0.015625,
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284 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJqAmwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a $2500$ kg demolition ball swings. The length of the swinging segment of cable is $17$ m. Find the period of the swinging, assuming that the system can be treated as a simple pendulum.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7.6 s B: 8.0 s ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.0289306640625,
0.006561279296875,
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0.0012969970703125,
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0.0224609375,
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0.03173828125,
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... |
285 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE0AmYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium. As the wave reaches a group of spectators, they stand with a cheer and then sit. At any instant, the width $w$ of the wave is the distance from the leading edge (people are just about to stand) to th... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0247802734375,
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0.00762939453125,
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0.036376953125,
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286 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAN6AlQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface. The waves are of two types: transverse waves traveling at \(v_t = 50\,\mathrm{m/s}\) and longitudinal waves traveling at \(v_l = 150\,\mathrm{m/s}\). If a sudden motion sends out such waves, a scorp... | D | Waves/Acoustics | Wave Properties | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.016845703125,
0.01165771484375,
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0.0015869140625,
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0.0111083984375,
0.0031585693359375,
0.0196533203125,
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0.00518798828125,
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0.002456665039... |
287 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHCA0QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time $t = 0$. The scale of the $x$ axis is set by $x_s = 0.80$ m. What is the amplitude of the wave?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.008... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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-0.0238037109375,
0.00360107421875,
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0.039794921875,
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0.0004730224609375,
0.019287109375,
0.0091552734375,
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288 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGmAhwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the transverse velocity $u$ versus time $t$ of the point on a string at $x = 0$, as a wave passes through it. The scale on the vertical axis is set by $u_s = 4.0$ m/s. The wave has the generic form $y(x, t) = y_m \sin(kx - \omega t + \phi)$. What then is $\phi$?Please directly answer the question and provi... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.026123046875,
0.000034332275390625,
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0.02294921875,
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0.02978515625,
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0.01458740234375,
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289 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHIArQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sinusoidal wave moving along a string is shown twice in figure, as crest $A$ travels in the positive direction of an $x$ axis by distance $d = 6.0$ cm in $4.0$ ms. The tick marks along the axis are separated by $10$ cm; height $H = 6.00$ mm. The equation for the wave is in the form $y(x, t) = y_m \sin(kx \pm \omega t... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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0.0103759765625,
-0.02478027343... |
290 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD0AjoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sinusoidal transverse wave of wavelength $20$ cm travels along a string in the positive direction of an $x$ axis. The displacement $y$ of the string particle at $x = 0$ is given in figure as a function of time $t$. The scale of the vertical axis is set by $y_s = 4.0$ cm. The wave equation is to be in the form $y(x, t... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0216064453125,
-0.00506591796875,
0.0013885498046875,
-0.006866455078125,
-0.0157470703125,
0.00274658203125,
0.014404296875,
0.0166015625,
-0.0262451171875,
0.000640869140625,
-0.01611328125,
0.03564453125,
-0.0228271484375,
0.01397705078125,
0.01202392578125,
-0.001190185546875,
... |
291 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG6AZwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sinusoidal transverse wave is traveling along a string in the negative direction of an $x$ axis. Figure shows a plot of the displacement as a function of position at time $t = 0$; the scale of the $y$ axis is set by $y_s = 4.0$ cm. The string tension is $3.6$ N, and its linear density is $25$ g/m. Find the period of ... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0086669921875,
0.02490234375,
-0.006256103515625,
0.009521484375,
0.003814697265625,
0.0108642578125,
-0.0172119140625,
-0.0238037109375,
0.0047607421875,
0.00762939453125,
-0.0157470703125,
0.021728515625,
-0.010009765625,
-0.00141143798828125,
0.01611328125,
-0.001434326171875,
-... |
292 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGWAbYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, string 1 has a linear density of \(3.00\,\mathrm{g/m}\), and string 2 has a linear density of \(5.00\,\mathrm{g/m}\). They are under tension due to the hanging block of mass \(M = 500\,\mathrm{g}\). Calculate the wave speed on string 2.Please directly answer the question and provide the correct OPTION LETTER... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0263671875,
0.005859375,
0.0146484375,
-0.00616455078125,
0.00396728515625,
0.01287841796875,
-0.0033721923828125,
0.0032958984375,
-0.034912109375,
0.0133056640625,
-0.0272216796875,
0.02099609375,
-0.003692626953125,
0.025634765625,
0.0166015625,
0.0159912109375,
-0.0155029296875... |
293 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFgBEIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A sinusoidal wave is sent along a string with a linear density of $2.0$ g/m. As it travels, the kinetic energies of the mass elements along the string vary. Figure gives the rate $dK/dt$ at which kinetic energy passes through the string elements at a particular instant, plotted as a function of distance $x$ along the s... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0186767578125,
0.0069580078125,
-0.01007080078125,
-0.001556396484375,
-0.001220703125,
0.0150146484375,
-0.0167236328125,
-0.0084228515625,
-0.019287109375,
0.00213623046875,
-0.0269775390625,
0.02734375,
-0.013671875,
0.0179443359375,
0.017822265625,
-0.00982666015625,
-0.0351562... |
294 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFqAfgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two sinusoidal waves with the same amplitude of $9.00$ mm and the same wavelength travel together along a string that is stretched along an $x$ axis. Their resultant wave is shown twice in figure, as valley $A$ travels in the negative direction of the $x$ axis by distance $d = 56.0$ cm in $8.0$ ms. The tick marks along... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0225830078125,
0.01123046875,
-0.0120849609375,
-0.0019683837890625,
0.00084686279296875,
0.005859375,
-0.01409912109375,
-0.020751953125,
-0.02099609375,
0.03076171875,
-0.0103759765625,
0.034423828125,
0.003021240234375,
-0.0025177001953125,
0.0115966796875,
0.016845703125,
-0.04... |
295 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACeAcIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A nylon guitar string has a linear density of $7.20$ g/m and is under a tension of $150$ N. The fixed supports are distance $D = 90.0$ cm apart. The string is oscillating in the standing wave pattern shown in figure. Calculate the frequency of the traveling waves whose superposition gives this standing wave.Please dire... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0089111328125,
0.004791259765625,
0.03271484375,
-0.0145263671875,
0.0004730224609375,
0.002777099609375,
-0.01409912109375,
-0.00164794921875,
-0.002532958984375,
-0.0076904296875,
-0.00543212890625,
0.006683349609375,
0.007568359375,
0.01226806640625,
0.00823974609375,
0.0189208984... |
296 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAcQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | For a particular transverse standing wave on a long string, one of the antinodes is at $x = 0$ and an adjacent node is at $x = 0.10$ m. The displacement $y(t)$ of the string particle at $x = 0$ is shown in figure, where the scale of the $y$ axis is set by $y_s = 4.0$ cm. What is the transverse velocity of the string pa... | D | Waves/Acoustics | Wave Properties | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.028076171875,
-0.00189208984375,
0.0006103515625,
-0.004913330078125,
-0.01043701171875,
0.00262451171875,
0.00506591796875,
0.0150146484375,
-0.0106201171875,
-0.00341796875,
-0.0279541015625,
0.026611328125,
-0.02978515625,
0.01055908203125,
0.0186767578125,
0.006988525390625,
-0... |
297 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFeAjIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two sinusoidal waves with the same amplitude and wavelength travel through each other along a string that is stretched along an \(x\) axis. Their resultant wave is shown twice in figure, as the antinode \(A\) travels from an extreme upward displacement to an extreme downward displacement in \(6.0\,\mathrm{ms}\). The ti... | D | Waves/Acoustics | Wave Properties | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0203857421875,
0.0019073486328125,
0.00482177734375,
0.016845703125,
-0.0069580078125,
0.017333984375,
-0.01446533203125,
-0.0198974609375,
-0.012451171875,
0.019775390625,
-0.00732421875,
0.030029296875,
-0.0162353515625,
0.017578125,
0.0037078857421875,
0.010009765625,
-0.0366210... |
298 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD0A2IDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Separation $L = 1.20$ m, linear density $\mu = 1.6$ g/m, and the oscillator frequency $f = 120$ Hz. The amplitude of the motion at $P$ is small enough for that point to be considered a node. A node also exists at $Q$. What mass $m$ allows the oscillator to set up the fourth harmonic on the string?Please directly answer... | D | Waves/Acoustics | Resonance and Harmonics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0220947265625,
0.005218505859375,
0.00153350830078125,
-0.008544921875,
-0.011474609375,
0.01446533203125,
0.00958251953125,
-0.0211181640625,
-0.00469970703125,
0.00008249282836914062,
-0.02685546875,
0.0283203125,
-0.0107421875,
-0.001800537109375,
0.017822265625,
0.02392578125,
... |
299 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFCAoIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, an aluminum wire, of length $L_1 = 60.0$ cm, cross-sectional area $1.00 \times 10^{-2}$ cm$^2$, and density $2.60$ g/cm$^3$, is joined to a steel wire, of density $7.80$ g/cm$^3$ and the same cross-sectional area. The compound wire, loaded with a block of mass $m = 10.0$ kg, is arranged so that the distance ... | D | Waves/Acoustics | Resonance and Harmonics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.031494140625,
0.021484375,
0.0126953125,
-0.0185546875,
-0.004608154296875,
0.028076171875,
0.005523681640625,
-0.0069580078125,
0.0140380859375,
-0.0103759765625,
-0.0164794921875,
0.0208740234375,
-0.00811767578125,
0.0186767578125,
0.00775146484375,
0.026611328125,
-0.0236816406... |
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