Transcript Physics 106P: Lecture 1 Notes

Physics 101: Lecture 33
Sound
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Today’s lecture will cover Textbook Sections 16.5 - 16.10
Physics 101: Lecture 33, Pg 1
From Last Time:
Speed of a wave is a constant, i.e. it only depends on the medium
through which it travels :
v=/T=f
Speed of a transverse wave traveling along a string:
T
T
v

m/L

Physics 101: Lecture 33, Pg 2
Sound
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Sound is a longitudinal wave, created by a vibrating
object (e.g. , vocal cords, guitar string).
Sound needs a medium, it does not exist in vacuum.
Sound waves in air are traveling disturbances of varying
air pressure: slightly less (rarefication) and higher than
normal (condensation).
Each cycle of a sound wave consists of one rarefication
and condensation. The frequency is the number of
cycles per second that passes by a given location.
Human ear: frequency = 20 – 20,000 Hz
Loudness: amplitude of the pressure wave (air pressure
over distance). The larger the amplitude the larger the
sound.
Physics 101: Lecture 33, Pg 3
Speed of Sound
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Speed of a sound wave depends on the medium:
Ideal gas (adiabatic compression and expansion of
gas):
v = (g k T/m)1/2
g=cp/cv
Liquid (Bad=Bulk modulus, volume change under
adiabatic conditions):
v = (Bad/r)1/2
Solid Bars (Y=Young’s modulus):
v = (Y/r)1/2
Physics 101: Lecture 33, Pg 4
Concept Question
A sound wave having frequency f0, speed v0 and wavelength 0, is traveling
through air when in encounters a large helium-filled balloon. Inside the balloon
the frequency of the wave is f1, its speed is v1, and its wavelength is 1
Compare the frequency of the sound wave inside and outside the balloon
1. f1 < f0
2. f1 = f0
correct
3. f1 > f0
f0 f1
Physics 101: Lecture 33, Pg 5
Concept Question
A sound wave having frequency f0, speed v0 and wavelength 0, is traveling
through air when in encounters a large helium-filled balloon. Inside the balloon
the frequency of the wave is f1, its speed is v1, and its wavelength is 1
Compare the speed of the sound wave inside and outside the balloon
1. v1 < v0
2. v1 = v0
3. v1 > v0
correct
V0=343m/s
V1=965m/s
Physics 101: Lecture 33, Pg 6
Concept Question
A sound wave having frequency f0, speed v0 and wavelength 0, is traveling
through air when in encounters a large helium-filled balloon. Inside the balloon
the frequency of the wave is f1, its speed is v1, and its wavelength is 1
Compare the wavelength of the sound wave inside and outside the balloon
1. 1 < 0
2. 1 = 0
3. 1 > 0
correct
0
1
=v/f
Physics 101: Lecture 33, Pg 7
Sound Intensity
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Amount of energy transported by a sound wave per
second is called power of the wave:
Power = energy/time
SI unit: [J/s= W]
Sound intensity measures the sound power that passes
Perpendicular trough a surface A per surface area:
I = P/A
SI unit: [W/m2]
Decibels (dB) are used to compare two sound intensities:
b = 10 dB Log (I/I0)
I0= threshold of hearing
Physics 101: Lecture 33, Pg 8
Concept Question
Suppose you are standing a distance D away from a speaker that is radiating
sound in a spherically uniform way. You walk away from the speaker until the
loudness of the sound is reduced by a factor of two. About how far from the
speaker are you now (neglecting any reflections from the ground)?
1. 10D
2. 4D
3. 3D
correct
4. 2D
Physics 101: Lecture 33, Pg 9
Speaker radiating power P
Changing I by 10 will change
loudness by 2 (10 dB)
I1 = P/(4pD12)
D1
We want I1/I2 = 10
I2 = P/(4pD22)
D2
I1
P

I 2 4pD12
P
4pD22

D22
D12
D22
D12
 10
D2  10D1  3.16 D1
Physics 101: Lecture 33, Pg 10
Doppler Effect
The wavelength of a sound wave of a source moving
with speed vs is shortened in front of the source by
’=-vs T
and lengthened behind the source by
’=+vs T
Thus, the frequency of the sound perceived by a
stationary observer in front of the source is
f0 = v/’ = fs / (1-vs/v)
=> f0 > fs
and behind the source
f0 = v/’ = fs / (1+vs/v)
=> f0 < fs
v: speed of sound
vs: speed of source
fs: frequency emitted by the source
f0: frequency heard by the observer
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Physics 101: Lecture 33, Pg 11
Concept Question
A: You are driving along the highway at 65 mph, and behind you a police car, also
traveling at 65 mph, has its siren turned on.
B: You and the police car have both pulled over to the side of the road, but the
siren is still turned on.
In which case does the frequency of the siren seem higher to you?
1. Case A
f
f’
2. Case B
v
3. same
correct
vs
vo
vo
f'
v

f 1  vs
v
1
Physics 101: Lecture 33, Pg 12