Physics 135A

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Physics 135A

• Physics 135A
• Lecture 22 Sound
• Dr. Z. Gong

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Physics 135A
Administrative Information

• Homework Set 10 is due next Tuesday. Those who
  turn in today will get 10 extra credit.
• 2nd Midterm will be returned next Tuesday.

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Physics 135A
Review -1

• Damped harmonic motion
• Underdamped, Overdamped and Critical damping
• Resonance when the frequency of the external
  force is very close to the natural frequency of
  the system, the overall vibration is dramatically
  enlarged
• Wave carries energy from one place to another,
  but medium is not moving with the wave.
• The source of wave is a vibration.

t
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Physics 135A
Review -2

• The wave velocity is equal to the wavelength over
  the period
• The velocity for the transverse wave is
• where FT is the tension force
• For solid rod the velocity of the longitudinal
  wave is
• , where E is the elastic modulus or

Wavelength ?
Amplitude
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Physics 135A
Physics 135A
Review -3

• Energy transported by a wave is proportional to
  the square of the amplitude.
• For a spherical wave the intensity of the wave is
• , so and
• Wave characteristics interference, reflection,
  refraction and diffraction

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Physics 135A
Physics 135A
Review -4

• When two waves traveling at opposite direction
  are in phase with each other, the resultant wave
  is the large-amplitude standing wave

First overtone or second harmonic ?L
Fundamental mode or first harmonic ?2L
Second overtone or third harmonic ?L/1.5
Third overtone or forth harmonic ?L/2
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Physics 135A
Physics 135A
Characteristics of sound

• Sound is a longitudinal wave
• Speed of sound is changing at different
  temperature
• Audible frequency range 20Hz 20000Hz
• Ultrasound frequency above 20000Hz
• Infrasound frequency below 20Hz, come from
  earthquake, volcano, thunder or some heavy
  machine. Might resonant with some organs in human
  body

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Physics 135A
Physics 135A
Ultrasound

• Ultrasound can penetrate in medium. Any object
  different from the medium will reflect portion of
  the sound wave back.
• Pulse-echo technology is used in sonar to detect
  submarine under the water, or in medicine in
  diagnosis and treatment
• Depend on the strength and frequency of the
  reflected wave, image inside the body can be
  deduced and used for diagnosis

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Physics 135A
Intensity of sound

• Intensity I energy transported by a wave per
  unit time cross unit area (W/m2).
• When the intensity of a sound is 10 times
  stronger, the loudness is doubled.
• The intensity of sound is also described in the
  unit of decibel (dB) defined as
• where

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Physics 135A
Example -1
A jet plane emits 5.0105 J of sound energy per
second. What is the intensity level 30m away? Air
absorbs sound at a rate of 7dB/km calculate what
the intensity level will be 1.0km and 5.0km away
from the jet plane.
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Physics 135A
Example -1
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Physics 135A
Source of sound

• Wave is generated by vibration.
• In music instrument standing waves are produced
  and the sources vibrate at their natural resonant
  frequency
• Fingered string has shorter resonant length and
  hence higher resonant frequency
• Sounding box is used as a mechanical amplifier to
  increase the loudness of the sound

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Physics 135A
Open tube

• At the open end of a music instrument the
  pressure reaches zero while air displacement
  reaches maximum

Pressure
Displacement
Fundamental mode ?2L
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Physics 135A
Close tube

• At the close end of a music instrument the
  pressure reaches maximum while air displacement
  reaches zero

Pressure
Displacement
Fundamental mode ?4L
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Physics 135A
Example -2
A uniform narrow tube 1.80m long is open at both
ends. It resonates at two successive harmonic
frequency of 275Hz and 330Hz. What is the speed
of sound in the gas in the tube? If the first
resonant frequency is n f1 then the next
successive resonant frequency is (n1) f1. So
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Physics 135A
Interference Beat

• When two sounds with different frequency meet,
  they will interfere with each other
• If the amplitude of the two waves are the same,
  then beat will generate

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Physics 135A
Doppler effect

• When the source of the sound is moving, the
  frequency at the receiver end will be different
  depending on whether the source is moving towards
  or away from the receiver.

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Physics 135A
Doppler effect

• When the source move towards the receiver, it
  takes less time for the next wave front to reach
  the receiver
• When the source move away from the receiver, it
  takes longer time for the next wave front to
  reach the receiver

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Physics 135A
Doppler effect coming
receiver
vs
source
vs
source
d
d
receiver
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Physics 135A
Doppler effect leaving
vs
receiver
source
d
vs
source
d
receiver
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Physics 135A
Example -3
Two loudspeakers are at opposite ends of a
railroad car as it moves past a stationary
observer at 10m/s. If they have identical sound
frequency of 200Hz. What is the beat frequency
hear by the observer when he is standing at the
following locations?
A
B
C
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Physics 135A
Example -3
At location A both of the loudspeakers are
leaving the person. The frequency shift is the
same. Therell be no beating. Similar situation
for location C.
A
B
C
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Physics 135A
Example -3
f2
f1
B