Chapter 15: SoundsChapter 15: Sounds
Properties of Sound:
1. Propagates in a longitudinal wave.
2. Alternating series of high pressure(compression) and low pressure(rarefaction).
Compressions and rarefactions
3. Speed defined by the wavelength andfrequency of a wave.
v = wavelength x frequency
a. wavelength: distance betweencompressions.
b. frequency (Hz): the number ofoscillations in time.
VelocityVelocity
Characteristics of the velocity of sound:
1. depends on temperature and medium
a. vacuum: no sound
b. cool air moves slower than warm air due to refraction (bends more in cool air) ie: ‘Red October’
c. normal 343 m/s @ 20oC and 1 atm or 331 m/s + (0.6 m/s ) T = 343 m/s
d. exhibits properties of reflection, refraction, interference, and diffraction
e. has areas of cancellation (nodescalled the ‘dead-spot’.Area where thewaves cancel.
f. Speed of sound depends on the the elasticity of the medium.
g. Sound travels 4x faster in liquids and 15x faster in solids as compared to air.
h. Properties that affect the speed of sound in air are
(1) pressure,
(2) denisity of the medium and
(3) the molecular mass of the medium.
SamplerSampler
1.A sound wave has a frequency of 261.6 Hz at20oC. What is the wavelength?
ans: 1.31 m
2. Sound with a frequency of 261.6 Hz travelsthrough water at a speed of 1435 m/s. Findthe wavelength in water?
ans: 5.485 m
3. Find the frequency of a sound wave at 20oCwith a wavelength of 0.667 m?
ans: 514 Hz
HW: #1-5, p 405 and #31 & 33, p424
The Doppler ShiftThe Doppler Shift
The apparent shift in frequency as a soundsource approaches a listener. Note a decreasewavelength is an increase in frequency.
The Doppler ShiftThe Doppler Shift
Equation:
fd = fs [ v + vd / v – vs ]
fd = frequency detected
fs = frequency from the source
v = standard velocity of sound in air @ 20oC
vd = Speed of the detector (person hearing thesound)
vs = speed from the source
Doppler ShiftDoppler Shift
A train whistles sounds at a frequency of 500 Hzas it approaches the terminal traveling at 40 m/s.A person at the terminal at rest would detect afrequency of what?
Relationship Pitch and FrequencyRelationship Pitch and Frequency
Pitch and frequency are the same
Octave: frequency changes in a 2:1 ratio
For every doubling of frequency, the octavechange by 1
2(f) = 1 ovtave higher
½(f) = 1 octave lower
C @ 262 Hz = C @ 523 or 523/2 = 262
F @ 349.2 Hz = 698.4 Hz or 698.4/2 = 349.2
LoudnessLoudness
The amplitude of the wave defines the loudnessof the sound.
Loudness is measured in decibels (dB). This unitis derived from the ratio of the pressure ofthe sound to the pressure of the lightestsound
ResonanceResonance
Sound is produced by the vibration ofmatter. If the vibration of the sound isequal to the natural vibration of thematerial, then the wave vibration isadditive.
Results in a standing wave
Closed-end ResonatorClosed-end Resonator
Tube with one end closed. Vibrations travel down the column and then reflectback. When the vibrations are in phase, ‘resonance’ occurs at a region of highpressure(gets louder) .
L = λ/4 L = v / 2f λ = 4L
L = 3λ/4 λ = 4L/3
L = 5λ/4 λ = 4L/5
Resonance Spacing = λ/2
L = v / 2f from a v = λf equation
Open-ended ResonanceOpen-ended Resonance
Both end at open: In phase vibrations occur ata region of lower pressure.
First Harmonic:L = λ / 2λ = 2L
Second Harmonic:L = ʎλ = L
Third Harmonics:L = 3λ/2λ = 2L/3
Open and Closed Ended ResonatorOpen and Closed Ended Resonator
SamplerSampler
1. An automatic focus camera is able to focus onobjects by use of an ultrasonic sound wave. Thecamera sends out sound waves which reflect offdistant objects and return to the camera. A sensordetects the time it takes for the waves to return andthen determines the distance an object is from thecamera. If a sound wave (speed = 340 m/s) returns tothe camera 0.150 seconds after leaving the camera,how far away is the object?
Ans: 25.5 m
2. The annoying sound from a mosquito isproduced when it beats its wings at theaverage rate of 600 wingbeats per second.
What is the frequency in Hertz of the soundwave?
Ans: 600 Hz
Assuming the sound wave moves with avelocity of 340 m/s, what is the wavelength ofthe wave?
Ans: 0.567 m
3. Doubling the frequency of a wave sourcedoubles the speed of the waves. True orFalse?
Ans: False, 2x frequency = ½ wavelength
Speed is uneffected by frequency
4. Playing middle C on the piano keyboardproduces a sound with a frequency of 256Hz. Assuming the speed of sound in air is 345m/s, determine the wavelength of the soundcorresponding to the note of middle C.
Ans: 1.35 m
5. An elephant produces a 10 Hz sound wave.Assuming the speed of sound in air is 345 m/s,determine the wavelength of this infrasonicsound wave.
Ans: 34.50m
6. Determine the speed of sound on a coldwinter day in Glenview (T=3 C).
Ans: 332.8 m/s
7. Two sound waves are traveling through acontainer of nitrogen gas. Wave A has awavelength of 1.5 m. Wave B has awavelength of 4.5 m. The velocity of wave Bmust be __________ the velocity of waveA.
a. one-ninth
b. one-third
c. the same as
d. three times larger than
Ans: c , the medium did not change
8. Two sound waves are traveling through acontainer of nitrogen gas. Wave A has awavelength of 1.5 m. Wave B has a wavelengthof 4.5 m. The frequency of wave B must be__________ the frequency of wave A.
a. one-ninth
b. one-third
c. the same as
d. three times larger than
Ans: b, increase λ, decrease f