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wavelength : distance between adjacent identical parts of a wave
https://openstax.org/books/university-physics-volume-1/pages/16-key-terms
A wave is a disturbance that moves from the point of origin with a wave velocityv.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
A wave has a wavelengthλλ, which is the distance between adjacent identical parts of the wave. Wave velocity and wavelength are related to the wave’s frequency and period byv=λT=λf.v=λT=λf.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Mechanical waves are disturbances that move through a medium and are governed by Newton’s laws.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Electromagnetic waves are disturbances in the electric and magnetic fields, and do not require a medium.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Matter waves are a central part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
A transverse wave has a disturbance perpendicular to the wave’s direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
A wave is an oscillation (of a physical quantity) that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both up and down and back and forth, around an equil...
https://openstax.org/books/university-physics-volume-1/pages/16-summary
A snapshot of a sinusoidal wave at timet=0.00st=0.00scan be modeled as a function of position. Two examples of such functions arey(x)=Asin(kx+ϕ)y(x)=Asin(kx+ϕ)andy(x)=Acos(kx+ϕ).y(x)=Acos(kx+ϕ).
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Given a function of a wave that is a snapshot of the wave, and is only a function of the positionx, the motion of the pulse or wave moving at a constant velocity can be modeled with the function, replacingxwithx∓vtx∓vt. The minus sign is for motion in the positive direction and the plus sign for the negative direct...
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The wave function is given byy(x,t)=Asin(kx−ωt+ϕ)y(x,t)=Asin(kx−ωt+ϕ)wherek=2π/λk=2π/λis defined as the wave number,ω=2π/Tω=2π/Tis the angular frequency, andϕϕis the phase shift.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The wave moves with a constant velocityvwvw, where the particles of the medium oscillate about an equilibrium position. The constant velocity of a wave can be found byv=λT=ωk.v=λT=ωk.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The speed of a wave on a string depends on the linear density of the string and the tension in the string. The linear density is mass per unit length of the string.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
In general, the speed of a wave depends on the square root of the ratio of the elastic property to the inertial property of the medium.
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The speed of a wave through a fluid is equal to the square root of the ratio of the bulk modulus of the fluid to the density of the fluid.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The speed of sound through air atT=20°CT=20°Cis approximatelyvs=343.00m/s.vs=343.00m/s.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The energy and power of a wave are proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The time-averaged power of a sinusoidal wave on a string is found byPave=12μA2ω2v,Pave=12μA2ω2v,whereμμis the linear mass density of the string,Ais the amplitude of the wave,ωωis the angular frequency of the wave, andvis the speed of the wave.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Intensity is defined as the power divided by the area. In a spherical wave, the area isA=4πr2A=4πr2and the intensity isI=P4πr2.I=P4πr2.As the wave moves out from a source, the energy is conserved, but the intensity decreases as the area increases.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Superposition is the combination of two waves at the same location.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Constructive interference occurs from the superposition of two identical waves that are in phase.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Destructive interference occurs from the superposition of two identical waves that are180°(πradians)180°(πradians)out of phase.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
The wave that results from the superposition of two sine waves that differ only by a phase shift is a wave with an amplitude that depends on the value of the phase difference.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
A standing wave is the superposition of two waves which produces a wave that varies in amplitude but does not propagate.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Nodes are points of no motion in standing waves.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
An antinode is the location of maximum amplitude of a standing wave.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Normal modes of a wave on a string are the possible standing wave patterns. The lowest frequency that will produce a standing wave is known as the fundamental frequency. The higher frequencies which produce standing waves are called overtones.
https://openstax.org/books/university-physics-volume-1/pages/16-summary
Δ P = Δ P max sin ( k x ∓ ω t + ϕ ) Δ P = Δ P max sin ( k x ∓ ω t + ϕ )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
s ( x , t ) = s max cos ( k x ∓ ω t + ϕ ) s ( x , t ) = s max cos ( k x ∓ ω t + ϕ )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
v = f λ v = f λ
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
v = B ρ v = B ρ
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v = Y ρ v = Y ρ
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
v = γ R T M v = γ R T M
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
v = 331 m s T K 273 K = 331 m s 1 + T C 273 ° C v = 331 m s T K 273 K = 331 m s 1 + T C 273 ° C
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
I 2 = I 1 ( r 1 r 2 ) 2 I 2 = I 1 ( r 1 r 2 ) 2
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
I = 〈 P 〉 A I = 〈 P 〉 A
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I = ( Δ p max ) 2 2 ρ v I = ( Δ p max ) 2 2 ρ v
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
β ( d B ) = 10 log 10 ( I I 0 ) β ( d B ) = 10 log 10 ( I I 0 )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
λ n = 4 n L , n = 1 , 3 , 5 ,… λ n = 4 n L , n = 1 , 3 , 5 ,…
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f n = n v 4 L , n = 1 , 3 , 5 ,… f n = n v 4 L , n = 1 , 3 , 5 ,…
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
λ n = 2 n L , n = 1 , 2 , 3 ,… λ n = 2 n L , n = 1 , 2 , 3 ,…
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f n = n v 2 L , n = 1 , 2 , 3 ,… f n = n v 2 L , n = 1 , 2 , 3 ,…
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f beat = | f 2 − f 1 | f beat = | f 2 − f 1 |
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f o = f s ( v v ∓ v s ) f o = f s ( v v ∓ v s )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f o = f s ( v ± v o v ) f o = f s ( v ± v o v )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
f o = f s ( v ± v o v ∓ v s ) f o = f s ( v ± v o v ∓ v s )
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
M = v s v M = v s v
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
sin θ = v v s = 1 M sin θ = v v s = 1 M
https://openstax.org/books/university-physics-volume-1/pages/17-key-equations
beat frequency : frequency of beats produced by sound waves that differ in frequency
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
beats : constructive and destructive interference of two or more frequencies of sound
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
bow wake : v-shaped disturbance created when the wave source moves faster than the wave propagation speed
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
Doppler effect : alteration in the observed frequency of a sound due to motion of either the source or the observer
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
Doppler shift : actual change in frequency due to relative motion of source and observer
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
fundamental : the lowest-frequency resonance
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
harmonics : the term used to refer collectively to the fundamental and its overtones
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
hearing : perception of sound
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
loudness : perception of sound intensity
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
notes : basic unit of music with specific names, combined to generate tunes
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overtones : all resonant frequencies higher than the fundamental
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
phon : numerical unit of loudness
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
pitch : perception of the frequency of a sound
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
shock wave : wave front that is produced when a sound source moves faster than the speed of sound
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
sonic boom : loud noise that occurs as a shock wave as it sweeps along the ground
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
sound : traveling pressure wave that may be periodic; the wave can be modeled as a pressure wave or as an oscillation of molecules
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
sound intensity level : unitless quantity telling you the level of the sound relative to a fixed standard
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
sound pressure level : ratio of the pressure amplitude to a reference pressure
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
timbre : number and relative intensity of multiple sound frequencies
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
transducer : device that converts energy of a signal into measurable energy form, for example, a microphone converts sound waves into an electrical signal
https://openstax.org/books/university-physics-volume-1/pages/17-key-terms
Sound is a disturbance of matter (a pressure wave) that is transmitted from its source outward. Hearing is the perception of sound.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Sound can be modeled in terms of pressure or in terms of displacement of molecules.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The human ear is sensitive to frequencies between 20 Hz and 20 kHz.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The speed of sound depends on the medium and the state of the medium.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
In a fluid, because the absence of shear forces, sound waves are longitudinal. A solid can support both longitudinal and transverse sound waves.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
In air, the speed of sound is related to air temperatureTbyv=331msTK273K=331ms1+TC273°C.v=331msTK273K=331ms1+TC273°C.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
vis the same for all frequencies and wavelengths of sound in air.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
IntensityI=P/AI=P/Ais the same for a sound wave as was defined for all waves, wherePis the power crossing areaA. The SI unit forIis watts per meter squared. The intensity of a sound wave is also related to the pressure amplitudeΔp:Δp:I=(Δp)22ρv,I=(Δp)22ρv,whereρρis the density of the medium in which the sound w...
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Sound intensity level in units of decibels (dB) isβ(dB)=10log10(II0),β(dB)=10log10(II0),whereI0=10−12W/m2I0=10−12W/m2is the threshold intensity of hearing.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The perception of frequency is pitch. The perception of intensity is loudness and loudness has units of phons.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Unwanted sound can be reduced using destructive interference.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Sound has the same properties of interference and resonance as defined for all waves.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Some musical instruments can be modeled as pipes that have symmetrical boundary conditions: open at both ends or closed at both ends. Other musical instruments can be modeled as pipes that have anti-symmetrical boundary conditions: closed at one end and open at the other.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Some instruments, such as the pipe organ, have several tubes with different lengths. Instruments such as the flute vary the length of the tube by closing the holes along the tube. The trombone varies the length of the tube using a sliding bar.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
String instruments produce sound using a vibrating string with nodes at each end. The air around the string oscillates at the frequency of the string. The relationship for the frequencies for the string is the same as for the symmetrical boundary conditions of the pipe, with the length of the pipe replaced by the lengt...
https://openstax.org/books/university-physics-volume-1/pages/17-summary
When two sound waves that differ in frequency interfere, beats are created with a beat frequency that is equal to the absolute value of the difference in the frequencies.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The actual change in frequency is called the Doppler shift.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The Mach number is the velocity of a source divided by the speed of sound,M=vsv.M=vsv.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
When a sound source moves faster than the speed of sound, a shock wave is produced as the sound waves interfere.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
A sonic boom is the intense sound that occurs as the shock wave moves along the ground.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
The angle the shock wave produces can be found assinθ=vvs=1M.sinθ=vvs=1M.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
A bow wake is produced when an object moves faster than the speed of a mechanical wave in the medium, such as a boat moving through the water.
https://openstax.org/books/university-physics-volume-1/pages/17-summary
Δ L = α L Δ T Δ L = α L Δ T
https://openstax.org/books/university-physics-volume-2/pages/1-key-equations
Δ A = 2 α A Δ T Δ A = 2 α A Δ T
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Δ V = β V Δ T Δ V = β V Δ T
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Q = m c Δ T Q = m c Δ T
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Q cold + Q hot = 0 Q cold + Q hot = 0
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Q = m L f Q = m L f
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Q = m L v Q = m L v
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P = k A ( T h − T c ) d P = k A ( T h − T c ) d
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