PHY238Y
Lecture 13
The Doppler Effect
References:
Halliday, Resnick, Walker: Fundamentals of Physics, 6th ed., Wiley 2003, Chapter 18 (18.8)
Hallett et al.: Physics for the life sciences, 4th ed., 2003, Ch.2 (2.7)
Some of the pictures were taken from Hyper Physics:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/soucon.html#soucon
Thanks to dr. Rod Nave for the permission to use the above resource
PHY238Y
Lecture 13
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Hearing: pressure in the cochlear liquid vs. pressure on the eardrum
(does human ear really amplifies sound?)
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Example (Ear amplifier)
1) Calculate the maximum net force on an eardrum due to a sound wave having a
maximum pressure of 2* 10-3 N/m2, if the diameter of the eardrum is 0.0085m.
2) Assuming the mechanical advantage of the hammer, anvil and stirrup is 2, calculate
the pressure created on the oval window (Ao = 0.03cm2)
3) Assuming the acoustic impedance of air Zair = 416 N*s/m3; and water
Zwater = 1.48*106 N*s/m3, calculate the relative transmission of the oval window to
sound waves (stransmitted/sincident).
PHY238Y
Lecture 13
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Absorption of sound: sound waves
produce molecular motion in the
material they propagate;
Friction reduces intensity by
energy dissipation.
Inside a medium:
I ( x)  I 0 e
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
x
x0
where x0 is the attenuation length
The attenuation length x0
depends strongly on: frequency
and the type of medium involved.
PHY238Y
Lecture 13
Attenuation of sound waves in various media
Material
Frequency (Hz)
Attenuation length
(mm)
Water
20
105
Water
106
20
Muscle
106
4*10-2
Bone
106
4*10-3
Bone
3.5*106
6*10-4
PHY238Y
Lecture 13
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Noise; noise reduction
Decrease of sound intensity:
I0
I  2 (inverse square law)
r
I  I 0e ar (dissipatio n due to medium)
where a is the characteristic dissipation coefficient for a given
medium
PHY238Y
Lecture 13
Sound source is stationary, observer (detector) is moving “into the waves”
PHY238Y
Lecture 13
Doppler effect for a source at rest (a) and moving (b).
Observer (detector) is at rest.
PHY238Y
Lecture 13
Both detector (observer) and source move
- Speed of sound is v
- Speed of the observer is v0
- Speed of the source is vs
PHY238Y
Lecture 13
PHY238Y
Lecture 13
PHY238Y
Lecture 13
PHY238Y
Lecture 13
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Is Doppler effect an illusion?
J.G. Neuhoff, M.K. McBeath: Am. J. Phys., Vol.65(7), 1997 found out that:
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Perceptual processing of frequency and intensity interact;
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Judgments about magnitude and direction of pitch change are influenced by
changes in loudness;
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The intensity of a Doppler-shifted tone rises as the source approaches;
loudness changes influence pitch change, so pitch is also perceived to rise
?