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Chapter 14Chapter 14
SoundSound
Using a Tuning Fork to Using a Tuning Fork to Produce a Sound WaveProduce a Sound Wave
A tuning fork will produce a pure musical A tuning fork will produce a pure musical notenote
As the tines vibrate, they disturb the air As the tines vibrate, they disturb the air near themnear them
As the tine swings to the right, it forces the As the tine swings to the right, it forces the air molecules near it closer togetherair molecules near it closer together
This produces a high density area in the airThis produces a high density area in the air This is an area of compressionThis is an area of compression
As the tine moves toward the left, the air As the tine moves toward the left, the air molecules to the right of the tine spread molecules to the right of the tine spread outout
This produces an area of low densityThis produces an area of low density This area is called a This area is called a rarefactionrarefaction
Using a Tuning Fork, finalUsing a Tuning Fork, final
As the tuning fork continues to vibrate, a succession of As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the forkcompressions and rarefactions spread out from the fork
A sinusoidal curve can be used to represent the A sinusoidal curve can be used to represent the longitudinal wavelongitudinal wave Crests correspond to compressions and troughs to rarefactionsCrests correspond to compressions and troughs to rarefactions
Speed of SoundSpeed of Sound
In a liquid, the speed depends on the In a liquid, the speed depends on the liquid’s compressibility and inertialiquid’s compressibility and inertia
B is the Bulk Modulus of the liquidB is the Bulk Modulus of the liquid ρ is the density of the liquidρ is the density of the liquid Compares with other wave speed equationsCompares with other wave speed equations
Yv
Bv
propertyinertial
propertyelasticv
T
v
Sound in Solid: Wave on string: General:
Doppler Effect, Case 1Doppler Effect, Case 1 An observer is An observer is
moving toward a moving toward a stationary sourcestationary source
Due to his Due to his movement, the movement, the observer detects observer detects an additional an additional number of wave number of wave frontsfronts
The frequency The frequency heard is increasedheard is increased
F ig 1 4 .8 , p . 4 3 5
S lid e 1 2
Doppler Effect, Case 2Doppler Effect, Case 2
An observer is An observer is moving away from moving away from a stationary sourcea stationary source
The observer The observer detects fewer detects fewer wave fronts per wave fronts per secondsecond
The frequency The frequency appears lowerappears lower
F ig 1 4 .9 , p . 4 3 6
S lid e 1 3
Doppler Effect, Source in Doppler Effect, Source in MotionMotion
As the source moves As the source moves toward the observer (A), toward the observer (A), the wavelength received the wavelength received is shorter and the is shorter and the frequency increasesfrequency increases
As the source moves As the source moves away from the observer away from the observer (B), the wavelength (B), the wavelength received is longer and received is longer and the frequency is lowerthe frequency is lower
carhorn.wavcarhorn.wav
Doppler Effect, both Doppler Effect, both movingmoving
Both the source and the observer could be Both the source and the observer could be movingmoving
Use positive values of vUse positive values of voo and v and vss if the motion is if the motion is towardtoward Frequency appears higherFrequency appears higher
Use negative values of vUse negative values of voo and v and vss if the motion is if the motion is awayaway Frequency appears lowerFrequency appears lower
Ex. 14.6 pg. 438Ex. 14.6 pg. 438
s
o
vv
vvƒƒ'
Shock WavesShock Waves
A shock wave A shock wave results when the results when the source velocity source velocity exceeds the speed exceeds the speed of the wave itselfof the wave itself
The circles The circles represent the represent the wave fronts wave fronts emitted by the emitted by the sourcesource
Shock Waves, contShock Waves, cont
Tangent lines are drawn from STangent lines are drawn from Snn to the to the wave front centered on Swave front centered on Soo
The angle between one of these tangent The angle between one of these tangent lines and the direction of travel is given lines and the direction of travel is given by sin θ = v / vby sin θ = v / vss
The ratio v/vThe ratio v/vss is called the is called the Mach NumberMach Number The conical wave front is the The conical wave front is the shock waveshock wave Shock waves carry energy concentrated Shock waves carry energy concentrated
on the surface of the cone, with on the surface of the cone, with correspondingly great pressure variationscorrespondingly great pressure variations
Interference of Sound Interference of Sound WavesWaves
Sound waves interfereSound waves interfere Constructive interference occurs Constructive interference occurs
when the path difference between when the path difference between two waves’ motion is zero or some two waves’ motion is zero or some integer multiple of wavelengthsinteger multiple of wavelengths
path difference = nλpath difference = nλ Destructive interference occurs when Destructive interference occurs when
the path difference between two the path difference between two waves’ motion is an odd half waves’ motion is an odd half wavelengthwavelength
path difference = (n + ½)λpath difference = (n + ½)λ
Fig 14.15, p. 441
Slide 17
Fig 14.15, p. 441
Slide 17
H
LHH
H
H
H
LL
L
LL
H
HH
H
L
LL
L
BeatsBeats BeatsBeats are alternations in loudness, due to are alternations in loudness, due to
interferenceinterference Waves have slightly different frequencies and Waves have slightly different frequencies and
the time between constructive and destructive the time between constructive and destructive interference alternatesinterference alternates
ffbeatbeat = |f = |f11-f-f22||
Standing WavesStanding Waves
When a traveling wave reflects When a traveling wave reflects back on itself, it creates traveling back on itself, it creates traveling waves in both directionswaves in both directions
The wave and its reflection interfere The wave and its reflection interfere according to the superposition according to the superposition principleprinciple
With exactly the right frequency, With exactly the right frequency, the wave will appear to stand stillthe wave will appear to stand still This is called a This is called a standing wavestanding wave
Standing Waves on a Standing Waves on a StringString
Nodes must occur Nodes must occur at the ends of the at the ends of the string because string because these points are these points are fixedfixed
F ig 1 4 . 1 6 , p . 4 4 2
S l i d e 1 8
Standing Waves on a Standing Waves on a String, cont.String, cont.
The lowest The lowest frequency of frequency of vibration (b) is vibration (b) is called the called the fundamental fundamental frequencyfrequency
F ig 14 .1 8 , p . 4 43
S lide 2 5
F
L2
nƒnƒ 1n
Resonance in Air Column Resonance in Air Column Open at Both EndsOpen at Both Ends
In a pipe open at both ends, the In a pipe open at both ends, the natural frequency of vibration natural frequency of vibration forms a series whose harmonics forms a series whose harmonics are equal to integral multiples of are equal to integral multiples of the fundamental frequencythe fundamental frequency
,3,2,1nL2
vnƒn
Tube Open at Both EndsTube Open at Both Ends
Standing Waves in Air Standing Waves in Air ColumnsColumns
If one end of the air column is If one end of the air column is closed, a node must exist at this closed, a node must exist at this end since the movement of the air end since the movement of the air is restrictedis restricted
If the end is open, the elements of If the end is open, the elements of the air have complete freedom of the air have complete freedom of movement and an antinode existsmovement and an antinode exists
Tube Closed at One EndTube Closed at One End
Resonance in an Air Resonance in an Air Column Closed at One EndColumn Closed at One End
The closed end must be a nodeThe closed end must be a node The open end is an antinodeThe open end is an antinode
,5,3,1nL4
vnfn