Physics 2211, Spring 2002

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Physics 2211 Lecture 39Todays Agenda

• Sound Waves
• Doppler Effect

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Sound Waves

• Sound waves are longitudinal waves

• s is the displacement of the element of mass, dm,
  from its equilibrium point

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Speed of Sound

• The measure of compressibility of a material is
  the Bulk Modulus
• DP change of pressure on the material
• DV/V factional change of the materials volume
• The higher B, the more difficult it is to
  compress the material
• B 2 GN/m2 for water and 620 GN/m2 for diamond

• Speed of sound is
• In air (at T 200 C), v 343 m/s.

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Sound Intensity

• Express I in terms of maximum change in pressure,
  Pm

• Heuristic derivation
• Guess
• Do dimensional analysis
• Therefore,
• Speed does depends on elastic properties of
  medium!
• Therefore,
• Thus, I is

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Sound Intensity

• Examples

• Threshold of hearing

15 orders of magnitude

• Threshold of pain

• Jet Engine (near)

• Express I in decibels (dB)

• Threshold of hearing

• Threshold of pain

• Jet Engine (near)

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Aside The Decibel Scale
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Using dBs

• Converting from dB to linear
• Arithmetic operations with dBs
• Multiplication
• Division
• Raised to a power
• Example The sound intensity of a 120 dB jet
  engine is reduced by one half. What is its new
  sound intensity?
• Answer 117 dB

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Propagation of Sound Waves

• Intensity is the rate of flow of energy (i.e.,
  power) in the sound wave per unit area.
• Intensity power density (power per unit area)

Plane Waves
Isotropically-Radiating Source
Spherical Waves

• Intensity due to a point source

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Example

• During a 2001 Linkin Park concert, the sound
  intensity 46 m in front of the speaker system was
  120 dB (threshold of pain). How far way would
  one have to move in order for the sound intensity
  to drop to 90 dB (jackhammer level).

• The ratio of the final intensity, If , to the
  initial intensity, Ii ,is

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Doppler Effect

• Consider a sound source producing plane waves

• Now let the sound source move towards you with
  velocity us

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Doppler Effect

• Wavelength of sound wave has been shortened due
  to the movement of the sound source

• Therefore, the frequency of the sound wave
  increases

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Doppler Effect

• If the sound source is receding from you then

• Therefore, the frequency of the sound wave for a
  moving source is

• If you are moving as well with velocity ur, then
  the apparent frequency of the sound waves is

Note us and ur are relative to the medium (air).
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Doppler Effect for Light Waves(Electromagnetic
Waves)

• From the Special Theory of Relativity,

u is the relative velocity between light source
and you (receiver) and c is the speed of light (3
x 108 m/s).

• For u/v

one obtains
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Doppler Effect Example

• Radars transmit electomagnetic waves which
  reflect off an object and return to radars
  detector.

• If there is a relative speed, u, between the
  radar and the object, then there will be
• a Doppler shift, u/l, in the transmitted wave and
• a Doppler shift, u/l, in the received wave
  (reflecting object becomes a source).

• X-band (f 10 GHz) police radar

Therefore, Df is approximately 30 Hz for every 1
mph.
80 mph (radial velocity, u )
Df 2.4 kHz
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Doppler Effect Examples

• Pulse Doppler radars
• Weather (speed of hydrometeors)
• GMTI (ground moving target indication)
• AI (airborne interceptors)
• SAR (synthetic aperture radar)
• Red Shift of celestial bodies
• Supports big bang theory

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Albuquerque Airport

• 3 meter resolution, Ku band (15 GHz)
• http//www.sandia.gov/RADAR/sar_sub/images/

3 m SAR
Optical
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What the Albuquerque Airport Might Look Like on a
Cloudy Night

• 3 meter resolution, Ku band (15 GHz)
• http//www.sandia.gov/RADAR/sar_sub/images/

3 m SAR
Optical
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San Francisco, California

• SIR-C X-band SAR image
• http//www2.jpl.nasa.gov/files/images/browse/ac-sa
  nfr.gif

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Doppler Example

• An airplane is moving directly toward an airport
  at a speed speed of 242 m/s while emitting sound
  waves of frequency 1250 Hz.
• What is the frequency of the sound received at
  the airport?
• Some of the sound waves reflect from the airport
  terminal building and are received back at the
  airplane. What is the apparent frequency of this
  echo?

Now the airport terminal is the source and the
airplane is the receiver
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Recap of todays lecture

• Sound Waves
• Doppler Effect
• Study for Quiz 5