Doppler Effect Physics 202 Professor Lee Carkner Lecture 11.
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Transcript of Doppler Effect Physics 202 Professor Lee Carkner Lecture 11.
Doppler Effect
Physics 202Professor Lee
CarknerLecture 11
PAL #10 Music How much would your eardrum move
from a tuning fork sound? Example: f = 440 Hz, = 90 dB
= (10 dB) log (I/I0)
I = I0 10(/10)
I = I = 1X10-3 W/m2
We need to relate I to sm:I = ½ v2sm
2
sm = Air density = = 1.21 kg/m3
Velocity of sound = v = 343 m/s
PAL #10 Music (cont.)
sm = (I/(½ v(2f)2))½
sm = (1X10-3/(½)(1.21)(343)(2440)2)½
sm = Even the loudest sounds only produce
very small motions What if the distance is doubled?
Since I = Ps/4r2, then but sm => √I, so The displacement is ½ as great
The Doppler Effect
If there is any relative motion between the two, the frequency of sound detected will differ from the frequency of sound emitted
Stationary Source
Moving Source
How Does the Frequency Change?
If the source and the detector are moving closer together the frequency increases
If the source and the detector are moving further apart the frequency decreases
Doppler Effect
Doppler Effect and Velocity
The greater the change the larger the velocity
Let us consider separately the situations where either the source or the detector is moving and the other is not
Stationary Source, Moving Detector
In general f = v/ but if the detector is moving then the effective velocity is v+vD and the new frequency is:
but =v/f so,
If the detector is moving away from the
source than the sign is negative
Moving Source, Stationary Detector
In general = v/f but if the source is moving the wavelengths are smaller by vS/f
’ = v/f - vS /f
f’ = v / (v/f - vS/f)
The the source is moving away from the detector then the sign is positive
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formula:f’ = f ( v±vD / v±vS )
What sign should be used?
For motion toward the sign should be chosen to increase f
Remember that the speed of sound (v) will often be 343 m/s
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
This is dangerous because passing through the shockwave makes the plane hard to control
Doppler Effect for Light
However, at low speeds (u<<c, where u is the relative velocity between source and detector) the equations reduce to the classical form:
f’ = f (1 ± u/c)
u = () c c, the speed of light in vacuum, is constant (3 X 108 m/s)
Spectral Line Shifts
When we observe a spectrum of a object, we compare the observed wavelengths to standard ones
For objects moving away from us the spectral lines move to larger wavelengths
For objects moving towards us the spectral lines move to shorter wavelengths
Red Shifted Spectrum
Expansion of the Universe
All galaxies are moving away from all others
In the past, everything in the universe must have been much closer together
Summary: Sound Waves
Sound waves are longitudinal or pressure waves
The medium oscillates in the direction of travel
The speed of sound depends on the density and the bulk modulus (compressibility ) of the medium:
v = (B/)½
Summary: Wave Equations
The equations for the amplitude and pressure of a sound wave are:
s = sm cos (kx-t)
p = pm sin (kx-t)
pm = (v) sm
Waves from two sources will interfere based on the path length difference between the sources and detector
L = m (fully constructive)L = (m+½) (fully destructive)
Summary: Intensity and Music The intensity of sound falls off with a inverse
square law:I = Ps/4r2
I =½v2sm2
The sound level is: = (10 dB) log (I0/I)
Harmonic frequencies of a pipef = nv/2L (open at 2 ends)f = nv/4L (open at 1 end)
Beat frequency = fbeat = f1 - f2
Summary: Doppler Effect Relative motion together produces
an increase in frequency Relative motion apart produces a
decrease in frequencyf’ = f ( v±vD / v±vS )
For light:u = () c