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b) Which planet’s semi-major axis is the closest in length to its semi-minor axis? 06-PearsonPhys20-Chap06 7/24/08 12:56 PM Page 337 12. Three identical coins 24. A slingshot is used to propel a stone vertically C B A are placed on a rotating platter as shown. As the frequency of rotation increases, identify which coin... |
force that acts on an object results in a change in the object’s kinetic energy, what can be said about the nature of this force? 26. How do you calculate work from a force- displacement graph? 27. According to the work-energy theorem, how much work is done on an isolated system? 28. Does power affect the amount of wo... |
:56 PM Page 338 38. A force of 250 N [up] is applied to a mass of 15.0 kg over a displacement of 9.60 m [up]. (a) How much work does the force do on the mass? (b) What is the change in gravitational (c) potential energy? If it is an isolated system, explain the difference between the answers for (a) and (b). 39. A car ... |
ulum bob with a mass of 0.750 kg is initially at rest at its equilibrium position. You give the bob a push so that when it is at a height of 0.150 m above its equilibrium position it is moving at a speed of 2.00 m/s. (a) How much work did you do on the bob? If you pushed on the bob with a force of (b) 40.0 N parallel t... |
Unit III Circular Motion, Work, and Energy 06-PearsonPhys20-Chap06 7/24/08 12:56 PM Page 339 48. What is the average power output if an engine lifts a 250-kg mass a distance of 30.0 m in 20.0 s? 49. What is the effective power required to maintain a constant speed of 108 km/h if the force opposing the motion is 540 N ... |
B is connected to block C by a string that is 1.50 m long. Initially, the three blocks are touching each other. As the blocks move and the strings become taut, they end up as shown in diagram (b). Is this an isolated or a non-isolated system? Explain. (a) What is the speed of the blocks after the force has acted for t... |
An earthquake more than two thousand kilometres away sent this tsunami speeding across the Indian Ocean. Waves, a form of simple harmonic oscillations, can efficiently transport incredible amounts of energy over great distances. How does a wave move through its medium? How does understanding simple harmonic motion hel... |
4 that increasing the probe’s speed this way is referred to as gravity assist. The entire journey of 3 500 000 000 km took seven years. For this incredible feat to succeed, scientists had to know where the planets would be seven years in the future. How could they do this? They relied on the fact that planets follow p... |
-forth movements the toy makes in 10 s. These back-andforth movements are called oscillations. 4 Record the number of oscillations made by the toy. 5 Repeat steps 1 to 4 for each toy. For the yo-yo, first achieve a steady up-and-down rhythm. Then do steps 3 and 4, counting the up-and-down motions. This type of repetiti... |
One complete oscillation is called a cycle. Figure 7.3 The wings of a bee in flight make a droning sound because of their motion. oscillatory motion: motion in which the period of each cycle is constant info BIT Earthquake waves can have periods of up to several hundred seconds. (a) (b) (c) (d) (e) Figure 7.4 The bee’... |
plot period as a function of frequency. Use the following values of frequency: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If possible, print this graph, label it, and add it to your notes. What is the shape of this graph? info BIT A Formula 1 racecar has 10 cylinders but the engine size is limited to 3.0 L, no bigger than ma... |
. Read the procedure, then determine and label the controlled, manipulated, and responding variables. Materials and Equipment stopwatch chair basketball metre-stick tape Procedure 1 Copy Table 7.2 into your notes. ▼ Table 7.2 Bounce, Period, and Frequency Bounce Height (cm) Time for 20 Bounces (s) Period (s/bounce) Fre... |
it possible to increase the period of an oscillatory motion without increasing the frequency? Explain. 6. Give three examples of oscillatory motion that you have observed. Applications 7. What is the frequency of a swimming water toy that makes 20.0 kicking motions per second? 8. Do the oars on a rowboat move with 12.... |
on a swing does. A piston moves up and down in the cylinder of an engine. At the extreme of its motion, it stops for a brief instant as it reverses direction and begins to accelerate downward until it reaches the bottom of its stroke. There it stops again and accelerates back, just as the swing does. In order for the ... |
349 Questions 1. Determine the controlled, manipulated, and responding 4. Determine the slope of the line. What are the units of the slope? variables. 2. Plot a graph of force versus displacement. Be sure to use a scale that allows you to use the full graph paper. Draw a line of best fit. 3. What kind of relationship ... |
s law, which states: The deformation of an object is proportional to the force causing the deformation. Figure 7.7 Robert Hooke lived at the same time as Sir Isaac Newton. Figure 7.8 Hooke’s notes show the simple devices he used to derive his law. Chapter 7 Oscillatory motion requires a set of conditions. 349 07-Phys20... |
, the force required for the displacement is recorded. 350 Unit IV Oscillatory Motion and Mechanical Waves 07-Phys20-Chap07.qxd 7/24/08 1:09 PM Page 351 Figure 7.11 Graph of data from Table 7.3 Table 7.3 shows the data collected for this spring and the results plotted on the graph shown in Figure 7.11. ▼ Table 7.3 Data... |
shaking of an earthquake. The main building materials for the Jin Mao Tower are concrete and steel. Chapter 7 Oscillatory motion requires a set of conditions. 351 07-Phys20-Chap07.qxd 7/24/08 1:09 PM Page 352 Example 7.2 Practice Problems 1. A spring is stretched through several displacements and the force required is... |
line and solve for the slope using the equation below. Note the points used in the equation are not data points. slope k F x point 1 (0.10, 0.20) point 2 (0.30, 0.60) (0.60 N 0.20 N) (0.30 m 0.10 m) k 2.0 N/m Paraphrase The spring constant of the spring is 2.0 N/m. The Restoring Force Imagine that you have applied a f... |
is its spring constant? Answers 1. 26.4 N 2. 2.5 103 N/m Analysis and Solution Draw a diagram to represent the stretched spring. Displacement to the right is positive, so the restoring force is negative because it is to the left, according to Hooke’s law. kx F 30.0 45.0 N (1.50 m) N m The restoring force is 45.0 N [le... |
stretched as much. Remember that force varies directly with displacement. Figure 7.19(b) As the mass returns to its equilibrium position (x 0), it achieves its maximum velocity. It is moving toward the left (the negative direction), but the restoring force acting on it is zero because its displacement is zero. The mas... |
SHM is called a simple harmonic oscillator. simple harmonic motion: oscillatory motion where the restoring force is proportional to the displacement of the mass simple harmonic oscillator: an object that moves with simple harmonic motion Chapter 7 Oscillatory motion requires a set of conditions. 355 07-Phys20-Chap07.q... |
its initial displacement. Regardless of the position of the mass, the force of gravity remains constant but the tension of the spring varies. In the position shown in Figures 7.21(b) and (d), the net (restoring) force is zero. This is where the spring’s tension is equal and opposite to the force of gravity. In the pos... |
is attached to the free end of the spring system to pull it downward from the ceiling. What is the total displacement of the mass? Answers 1. 1.35 104 N/m 2. 2.3 m s and F g Given x 0.500 m m 510.0 g 0.5100 kg g 9.81 m/s2 Required spring constant (k) Analysis and Solution Draw a diagram to show the mass-spring system ... |
direction to the displacement. • At the extremes of SHM, the displacement is at its maximum and is referred to as the amplitude. At this point, force and acceleration are also at their maximum, and the velocity of the object is zero. • At the equilibrium position, the force and acceleration are zero, and the velocity ... |
much as 15 minutes a day. They used a series of special gears and weights that didn’t always produce a uniform rate of rotation — a necessity for an accurate mechanical clock. Huygens recognized that if he could take advantage of the uniform oscillations of a pendulum, he could produce a much better clock. When comple... |
increase and the restoring force (F R) becomes less and less. When it reaches the equilibrium position, no component of gravity is acting parallel to the motion of the bob, so the restoring force is zero, but the velocity has reached its maximum value. Figure 7.26(c) restoring force has also reached a maximum value bu... |
a graph of force versus displacement like those done for springs earlier in this chapter (e.g., Figure 7.11 on page 351). The displacement of the pendulum can be measured by its angle from the vertical. If the graph is linear, then the restoring force is proportional to the displacement, and the pendulum has moved in ... |
force for a pendulum bob of mass 100.0 g that has been pulled to an angle of 10.0 from the vertical. Given g 9.81 m/s2 m 100.0 g 0.1000 kg Required restoring force (FR) Analysis and Solution Draw a diagram of the pendulum in its displaced position to show the forces acting on the bob. left right 10.0° FT Fg Fg FR Figu... |
mass. Loosen the clamp and adjust the length of the thread so that it is the same length as for the previous mass. (Remember to measure length to the middle of the mass.) Repeat steps 5 to 7 until all the masses are used. Analysis 1. Determine the frequency and period of each mass. Record the numbers in your table. 2.... |
-g mass to the free end of the thread. 4 Measure the length of the thread from the clamp to the middle of the mass. Record this length at the top of Table 7.7. 5 Pull the mass on the thread back until it makes an angle of 5 with the vertical, as measured with the protractor. 6 Remove the protractor, and release the mas... |
scillatory Motion and Mechanical Waves 07-Phys20-Chap07.qxd 7/24/08 1:09 PM Page 365 7.2 Check and Reflect 7.2 Check and Reflect Knowledge 7. Two students are given the task of 1. The restoring force of a vertical mass- spring system is determined by the mass attached to the spring and the spring constant k. What two f... |
the spring be stretched when a 4.0-kg mass is attached to its free end? 6. An applied force of 25.0 N is required to compress a spring 0.20 m. What force will pull it to a displacement of 0.15 m? 10. Obtain three different types of rulers: plastic, metal, and wooden. Fix one end of each ruler to the side of a desk so ... |
and the acceleration. The only constant for a swinging tire is its period. In this section, you will mathematically analyze acceleration, velocity, and period for SHM in a mass-spring system, and then determine the period of a pendulum. Both mass-spring systems and pendulums are simple harmonic oscillators, as describ... |
the mass, so the acceleration changes throughout the entire motion as shown in Figure 7.29. Since acceleration of a simple harmonic oscillator is not uniform, only the instantaneous acceleration of the mass can be determined by equation 4. () () (b) (c) () Acceleration (a) (a) () (b) () Displacement () (c) x 0 The Rel... |
half of a complete oscillation from (a) to (b) to (c). Below the diagram are the acceleration-displacement and velocity-displacement graphs. The diagram of the oscillator and the graphs are vertically aligned so the graphs show you what is happening as the massspring system moves. In the diagram at the top of Figure 7.... |
Chap07.qxd 7/24/08 1:09 PM Page 369 Consider a vertical mass-spring system. A bungee jumper will experience a positive acceleration when she is below the equilibrium position and a negative acceleration when above it (Figures 7.33 and 7.34). (a) (b) (c) equilibrium x max x 0 x max a v a v a v Displacement Figure 7.33 D... |
). Kinetic energy has reached a maximum value (Ekmax has a maximum velocity. The potential energy is zero (x 0). ) because the oscillator Remember that the total energy of the system remains constant regardless of the oscillator’s position. The equation for the total energy is: ET Ep Ek The kinetic energy of the oscill... |
is positive and vice versa. Why? 2. Why is the velocity-time graph of a simple harmonic oscillator a curved line? 3. The acceleration-displacement graph and velocity-displacement graph are shown in Figure 7.32 on page 368 for half of an oscillation only. Sketch three more acceleration-displacement and velocitydisplace... |
oscillates with an amplitude of 1.12 m. What is its maximum speed? 3. An instructor sets up an oscillating vertical mass-spring system (k 6.05 N/m). The maximum displacement is 81.7 cm and the maximum speed is 2.05 m/s. What is the mass of the oscillator? Answers 1. 0.362 m [right] 2. 10.0 m/s 3. 0.961 kg Analysis and... |
the circular motion must match the amplitude of the oscillator. For example, look at Figure 7.38, where a mass moving in a circular path with a radius r is synchronized with a mass-spring simple harmonic oscillator. This illustration demonstrates how circular motion can be used to describe SHM. Figure 7.37 From a dist... |
oscillator (vmax), and the radius of the circle matches its amplitude. Therefore, we can customize the equation for the mass-spring oscillator: 2A T vmax (7) If we equate equation 5 and equation 7, we get: A k m 2A T We can then solve for T: A k m 2A T 2π k T T 2 m m k (8) This equation describes the period of a simpl... |
Which one has the longest period? They have the same period because displacement doesn’t affect the period of a simple harmonic oscillator. This relationship is true for any simple harmonic oscillator, including a pendulum with a small amplitude. It is easy enough to test. Take two pendulums with the same mass and len... |
03 N/m vmax 5.13 m/s Required period of the oscillations (T ) equilibrium Analysis and Solution To determine the period of the oscillator, you need to know the oscillator’s mass. Use the maximum speed equation (equation 5) to find the mass: Figure 7.42 EPmax Ekmax A2 2 k mv max 2 2 mv 2 max kA2 0.1225 m)2 5.03 m m 2 5.... |
sin in this equation: Fg sin. Use the Fg FR x l θ l x Recall also that in a mass-spring system, the restoring force is F kx. We want to solve for the period (T ), which is a scalar quantity, so the negative sign in Hooke’s law can be omitted. The two equations for restoring force can then be equated: Figure 7.43 For a... |
point, you can use a pendulum. If you manipulate equation 9 and solve for g, you get: g 42l T 2 (10) Due to the changing nature of Earth’s gravity, Christiaan Huygens’s pendulum clock (introduced in section 7.2) was only accurate if it was manufactured for a specific place. For example, pendulum clocks designed to ope... |
/kg [down] 2. 1.03 m 3. 1.79 s At the top of Mount Everest, a pendulum will swing with a slightly different period than at sea level. So a pendulum clock on Mount Everest, oscillating with a longer period than one at sea level, will report a different time. Huygens’s clocks also suffered from another problem: the pendu... |
circular path with a radius of 1.50 m at a constant speed of 5.00 m/s is synchronized with the mass-spring system. Determine the mass-spring system’s: 3. Describe the positions that a mass-spring system and pendulum are in when: (a) period (b) mass (a) acceleration is a maximum (b) velocity is a maximum (c) restoring ... |
Page 381 info BIT When you walk with a drink in your hand at the right speed, your motion creates resonance in the liquid. This makes waves that splash over the edge of the cup. To prevent this, people walk slowly so resonance doesn’t occur, often without knowing why this works. resonant frequency: the natural frequen... |
friction would very quickly stop the pendulum from swinging. To compensate for the effects of friction, he designed his clocks so that the pendulum was given a small push at just the right moment in its swing. The timing of these pushes coincided with the resonant frequency of the pendulum. By doing this, Huygens coul... |
ulum because the pendulum won’t be in the right position when the force is applied. The pendulum will bounce around but there will be no increase in its amplitude of vibration, and its motion will become harder to predict. The flowchart in Figure 7.46 on the next page summarizes the relationship between forced frequenc... |
or may be decreased. Is the forced frequency close to the resonant frequency? YES A small force is required to keep the object vibrating with the same amplitude. The force is increased. The amplitude of vibration increases. Figure 7.46 Flowchart of the effect of forced frequency on resonant amplitude Chapter 7 Oscilla... |
less, then pull back mass 2 and release it. Note the amplitude of vibration that mass 1 achieves. Questions Part A 1. At what thread length did mass 2 create the maximum oscillation of mass 1? Explain why this happened, in terms of frequency. 2. At what thread length did mass 2 create the minimum oscillation of mass 1?... |
to reduce the amplitude of resonance. Bridge designers make bridges more streamlined so that the wind passes over without imparting much energy. They also make bridges stiff, so a larger force is needed to create a large amplitude. The second-largest bridge in the world, the Great Belt East Bridge of Denmark is built ... |
, boat, and other equipment around the home. Yancey watched and helped his father, and during this time, his interest in mechanics grew. Not long after finishing high school, Yancey enrolled in the aircraft maintenance engineer program at the British Columbia Institute of Technology located in Burnaby. He is now qualif... |
available. They have an accuracy of about 1/2000 of a second a day. A quartz clock works on the principle of resonance. Inside each quartz clock is a tiny crystal of quartz. Quartz is a mineral that naturally forms into crystals. It also has a property unique to just a handful of materials: it will bend when a voltage... |
ates with a resonant frequency of about 30 kHz and operates at 1.5 V. A small microprocessor in the watch combines these oscillations to make one oscillation per second so the watch can display time in a meaningful way. The topic of resonant frequencies is large and can’t possibly be fully covered in this unit. You wil... |
6. Can a pendulum clock built to operate at the equator have the same accuracy at the North Pole? Explain. 7. What is damping? Use an example in your explanation. Applications 8. How could a person walking across a rope bridge prevent resonant vibration from building up in the bridge? 9. An opera singer can shatter a ... |
: in your answer. 2. (7.1) Under what conditions must a ball be bounced so it has oscillatory motion? 3. (7.2) What is the defining property of an elastic material? 4. (7.2) What force, or forces, act on an isolated, frictionless simple harmonic oscillator? 5. (7.2) State the directional relationship that exists betwee... |
distance of the mass above the floor? 18. Two different springs, A and B, are attached together at one end. Spring A is fixed to the wall as shown. The spring constant of A is 100.0 N/m and B is 50.0 N/m. What is the combined stretch of the two springs when a force of 25.0 N [right] is applied to the free end of sprin... |
and finds it is 1.79 s. What is the pendulum’s length? Extensions 27. A spring (k 10.0 N/m) is suspended from the ceiling and a mass of 250.0 g is hanging from the end at rest. The mass is pulled to a displacement of 20.0 cm and released. (a) What is the maximum velocity of the mass? (b) What is the period of oscillat... |
verse universal wave equation reflection interference acoustical resonance Doppler effect Learning Outcomes When you have finished this chapter, you will be able to: Knowledge describe how transverse and longitudinal waves move through a medium explain how the speed, wavelength, frequency, and amplitude of a wave are r... |
its operation dowel ( 1.5 cm in diameter) 2 stopwatches ruler, two paper clips light and stand to project waves onto screen screen (a large sheet of newsprint works well) Procedure 1 Set up the ripple tank as shown in Figure 8.2. The water should be about 1 cm deep. Make sure that energy-absorbing buffers are placed a... |
? Think About It 1. What differences and similarities are there between the ways energy is transmitted by waves and by matter? e SIM Find out more about waves in ripple tanks. Go to www.pearsoned.ca/school/ 2. What assumptions must be made to use water waves as a model for physicssource. sound waves? Discuss your answe... |
, even though the surfer is sliding down the front of the wave he never seems to get much closer to the bottom of the wave. It is a common misconception that the water in a wave moves in the direction in which the waves are travelling. This may be because waves arriving at the shoreline move water to and fro across the... |
create a continuous series of crests and troughs forming a wave train. Wave generators can act as a point source similar to the tip of a finger, or as a straight line source, similar to a dowel. In 8-1 QuickLab you measured the speed of a single pulse by observing its motion. However, because it is impossible to keep ... |
) Set up the ripple tank as shown in Figure 8.7. (b) When using motorized wave generators, it is important that the generator just barely contacts the surface of the water. It should never touch the tank during operation. Check with your instructor to make sure that your apparatus is properly assembled. CAUTION: Use ca... |
step 2 (b). Analysis 1. (a) When the incident wave train created by the point-source generator is passing through the reflected wave train, what happens to the waves in the region where they overlap? (b) Can you see the direction of the motion for both the incident and reflected wave trains? generator, what pattern do... |
the mathematical relationship between the volume of sound and the distance from the source, follow the links at www.pearsoned.ca/ school/physicssource. Chapter 8 Mechanical waves transmit energy in a variety of ways. 397 08-PearsonPhys20-Chap08 7/24/08 2:23 PM Page 398 light rays trough crest water ripple tank bottom ... |
S real source imaginary incident wave generated by S reflected portion of incident wave incident wave generated by S imaginary straight wave generator reflected wave front real straight wave generator incident wave from imaginary generator reflecting surface of barrier incident wave front Figure 8.11 When circular wav... |
a serious hazard in an area where electricity is being used. Vibrating the tank will generate unwanted waves that interfere with the desired observations. The wave generator should never touch the tank during operation. Procedure 1 Place small pads (about 8 mm thick) under the legs along one edge of the ripple tank so... |
wave fronts affected as they entered shallow water? (c) If so, how did the shape of the wave fronts change as they changed speed? 5. When a water wave moves toward a beach, how would the change in the depth of the water affect the motion of the wave? 8.1 Check and Reflect 8.1 Check and Reflect Knowledge 1. If a wave p... |
.13. In this section we will consider the characteristics of such waves. Transverse Pulses info BIT The ever-popular Slinky™ was invented in 1945 by Richard James, a naval engineer working on tension springs. The name comes from the Swedish for “sleek” or “sinuous.” Each Slinky™ is made from 80 feet (24.384 m) of wire.... |
set up a sequence in which the coils of the spring imitate the motion of your hand. This creates a moving pulse. l vhand 0 Chapter 8 Mechanical waves transmit energy in a variety of ways. 401 08-PearsonPhys20-Chap08 7/24/08 2:23 PM Page 402 Energy Changes During the Movement of a Pulse Along the pulse, energy is store... |
2:23 PM Page 403 8-4 Inquiry Lab 8-4 Inquiry Lab Pulses in a Spring, Part 1: Pulses in an Elastic Medium Required Skills Initiating and Planning Performing and Recording Analyzing and Interpreting Communication and Teamwork In this experiment, you will study how a pulse moves through a medium. Question What are the me... |
and then back to its original position. This pulse is called a longitudinal pulse, because its amplitude is along the direction of its motion. Repeat the pulse a few times to determine the nature of the motion of the spring as the pulse moves through it. Sketch and describe the motion of the coils as the pulse moves a... |
itudinal Waves If, instead of moving your hand across the line of the spring, you give the spring a sharp push along its length, you will observe that a pulse moves along the spring. This pulse is evidence of a longitudinal wave. The pulse is seen as a region where the coils are more tightly compressed followed by a re... |
end. Do this a few times to establish a consistent value. Record your results. Use the time and the distance between the hands to calculate the speed of the pulse. (b) Generate pulses by moving your hand to the side and back at different speeds (more quickly or more slowly). Measure the speed of each of these pulses. ... |
-Chap08 7/24/08 2:23 PM Page 406 Pulse Length and Speed Figure 8.18 The length (l) of the pulse depends on the speed (v) of the pulse and the time (t) taken to complete the pulse. e WEB To learn more about the way the structures of the human ear transfer sound waves, follow the links at www.pearsoned.ca/school/ physics... |
surface of water, or other liquids, where the waves are the result of gravitational potential energy rather than elastic potential energy. motion of water within wave Figure 8.19 406 Unit IV Oscillatory Motion and Mechanical Waves 08-PearsonPhys20-Chap08 7/24/08 2:23 PM Page 407 M I N D S O N Wave Motion in Fluids Wat... |
the midpoint of the spring (c) description of reflected pulse passing the midpoint of the spring Analysis and Solution (a) The length of the pulse can be found using l vt. l vt (0.80 s) 2.5 m s 2.0 m (b) The spring is defined as an ideal spring, so the amplitude of the pulse is constant. The amplitude at all points on... |
of water waves but are used throughout wave studies. For a water wave, the crest occurs where the medium is displaced above the equilibrium position, while a trough is the region displaced below the equilibrium position. However, for media such as springs, the terms crest and trough merely refer to two regions in the ... |
5.40 m/s, what is the wavelength? Given v 5.40 m/s f 2.00 Hz Required wavelength Analysis and Solution The variables (v, f, λ) are related by the universal wave equation. v f λ v λ f m 5.40 s 2.00 Hz 5.40 m s 2.00 1 s 2.70 m Paraphrase and Verify The wavelength is 2.70 m. Practice Problems 1. Orchestras use the note w... |
? 4. What determines the amount of energy stored in a wave? Applications 5. Sound waves travel through seawater at about 1500 m/s. What frequency would generate a wavelength of 1.25 m in seawater? 6. Temperature changes in seawater affect the speed at which sound moves through it. A wave with a length of 2.00 m, travel... |
other so that they reached the other person’s ears unchanged. How waves interact when they cross paths is well understood. When you observe two waves crossing in the ripple tank, things happen so quickly that it is difficult to see what is happening. Still, it is plain that the waves do pass through each other. By sen... |
spring takes on is predicted by the principle of superposition. This principle, based on the conservation of energy, makes it quite easy to predict the shape of the spring at any instant during which the pulses overlap. The displacement of the combined pulse at each point of interference is the algebraic sum of the di... |
of the reflected pulse must be the negative of the incident pulse. Hence, the reflected pulse must be inverted relative to the incident pulse. info BIT Since, at the point of reflection in the spring the system is basically an isolated system, all the energy in the incident pulse must be carried away by the reflected ... |
pattern and the length of the spring, the wavelength and the speed of the standing wave are easily calculated. For both parts, identify which are the controlled variables, manipulated variables, and responding variables. Part 1: Superposition and Interference of Pulses 1 (a) Place two parallel strips of tape on the fl... |
portion of the wave is passing through the incident wave. Discuss your observations with your lab team to come to a consensus on what is occurring. 414 Unit IV Oscillatory Motion and Mechanical Waves 08-PearsonPhys20-Chap08 7/24/08 2:23 PM Page 415 (c) Record your observations. Keep in mind what Analysis you observed ... |
To what does the speed of a standing wave refer? 4. Express the frequencies, for the different trials recorded in your data table, as ratios using simple whole numbers. Compare these ratios to the number of segments in which the spring oscillates for each trial. NOTE: The parts of a standing wave that remain motionles... |
. How is it possible for the two pulses to reappear as if from nothing? Where does the energy in the pulses go when the sum of the amplitudes is zero? Hint: It might help to think of the spring in terms of a system. Standing Waves and Resonance When two wave trains with identical wavelengths and amplitudes move through... |
occurs. The regions to the left and right of point A show a crest and a trough, respectively, with displacement of the resultant being twice that of the blue or purple waves. • Every time the wave trains move a further 1 λ along the spring, the 4 interference changes from constructive to destructive and vice versa. At... |
to oscillate around stationary points called nodes. The wavelength of a standing wave is the distance between alternate nodes or alternate antinodes. Figure 8.29 Standing waves occur in nature. This photograph shows a standing wave in a stream crossing a sandy beach in Scotland. e WEB Find out about the details of a s... |
of Washington (Figure 8.31). Opened in November 1940, the bridge was in operation only a few months before resonance ripped it apart. More recently, in June 2000, the newly opened Millennium Bridge in London had to be closed for modifications when the footsteps of pedestrians set up resonance patterns. Anyone who has ... |
is known as closed-pipe or closed-tube resonance. However, if the open end of the pipe coincides with the position of a node (destructive interference), then almost no sound can be heard because the source (tuning fork) and the standing wave are out of phase (Figure 8.33 (b) and (d)). (b) (a) R NR R (c) (d) Figure 8.3... |
is (a) the actual wavelength, and (b) the actual speed of sound? Chapter 8 Mechanical waves transmit energy in a variety of ways. 419 08-PearsonPhys20-Chap08 7/24/08 2:23 PM Page 420 Practice Problems 1. A tuning fork of frequency 512 Hz is used to generate a standing wave pattern in a closed pipe, 0.850 m long. A str... |
λ. Calculate the wavelength 4 and the speed of sound from that data. Assume that l 1 λ. Therefore, 4 λ 4l v fλ 4(0.675 m) 2.70 m (384 Hz)(2.70 m) 1037 m/s 1.04 103 m/s This value is larger than the speed of sound in air. If the speed of sound is not of the proper order of magnitude, then assume that the resonant point... |
and wavelength (). The wavelength is determined from the length of the pipe (l ) and the number of the resonant point as counted from the reflecting surface. Materials and Equipment tuning forks and tuning fork hammer or an audio frequency generator glass or plastic pipe tall cylinder Procedure 1 Assemble the apparatu... |
Page 422 ▼ Table 8.2 Resonant Points, Wavelength, and Speed of Sound First Resonant Point Second Resonant Point Third Resonant Point Frequency f (Hz) Wavelength 4l (m) Speed v (m/s) Wavelength 4l/3 (m) Speed v (m/s) Wavelength 4l/5 (m) Speed v (m/s) 5. Why should you measure the length of the column from the reflectin... |
info BIT Assume that the fundamental frequency is f. In physics and in music, the frequency 2f is called the first overtone; 3f is the second overtone, and so on. These frequencies are said to form a harmonic series. Thus, physicists may also refer to the fundamental frequency (f ) as the first harmonic, the frequency... |
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