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Music
Physics 202Professor Vogel (Professor Carknerrsquos notes
ed)Lecture 9
Music A musical instrument is a device for setting up standing
waves of known frequency A standing wave oscillates with large amplitude and so is loud
We shall consider an generalized instrument consisting of a pipe which may be open at one or both ends Like a pipe organ or a saxophone
There will always be a node at the closed end and an anti-node at the open end
Can have other nodes or antinodes in between but this rule must be followed Closed end is like a tied end of string open end is like a string
end fixed to a freely moving ring
Sound Waves in a Tube
Harmonics Pipe open at both ends
For resonance need a integer number of frac12 wavelengths to fit in the pipe Antinode at both ends
L = frac12 n v = ff = nv2L
n = 1234 hellip
Pipe open at one end For resonance need an integer number of frac14 wavelengths to
fit in the pipe Node at one end antinode at other
L = frac14 n v = ff = nv4L
n = 1357 hellip (only have odd harmonics)
Harmonics in
Closed and Open
Tubes
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Music A musical instrument is a device for setting up standing
waves of known frequency A standing wave oscillates with large amplitude and so is loud
We shall consider an generalized instrument consisting of a pipe which may be open at one or both ends Like a pipe organ or a saxophone
There will always be a node at the closed end and an anti-node at the open end
Can have other nodes or antinodes in between but this rule must be followed Closed end is like a tied end of string open end is like a string
end fixed to a freely moving ring
Sound Waves in a Tube
Harmonics Pipe open at both ends
For resonance need a integer number of frac12 wavelengths to fit in the pipe Antinode at both ends
L = frac12 n v = ff = nv2L
n = 1234 hellip
Pipe open at one end For resonance need an integer number of frac14 wavelengths to
fit in the pipe Node at one end antinode at other
L = frac14 n v = ff = nv4L
n = 1357 hellip (only have odd harmonics)
Harmonics in
Closed and Open
Tubes
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Sound Waves in a Tube
Harmonics Pipe open at both ends
For resonance need a integer number of frac12 wavelengths to fit in the pipe Antinode at both ends
L = frac12 n v = ff = nv2L
n = 1234 hellip
Pipe open at one end For resonance need an integer number of frac14 wavelengths to
fit in the pipe Node at one end antinode at other
L = frac14 n v = ff = nv4L
n = 1357 hellip (only have odd harmonics)
Harmonics in
Closed and Open
Tubes
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Harmonics Pipe open at both ends
For resonance need a integer number of frac12 wavelengths to fit in the pipe Antinode at both ends
L = frac12 n v = ff = nv2L
n = 1234 hellip
Pipe open at one end For resonance need an integer number of frac14 wavelengths to
fit in the pipe Node at one end antinode at other
L = frac14 n v = ff = nv4L
n = 1357 hellip (only have odd harmonics)
Harmonics in
Closed and Open
Tubes
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Harmonics in
Closed and Open
Tubes
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Adding Sound Waves
If two sound waves exist at the same place at the same time the law of superposition holds
This is true generally but two special cases give interesting results Adding harmonics Adding waves of nearly the same
frequency
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Adding Harmonics Superposition of two or more sound
waves that are all harmonics of the same
fundamental frequency one may be the fundamental
The sum is more complicated than a sine wave but the resultant wave oscillates at the
frequency of the fundamental simulation link
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Beat Frequency
You generally cannot tell the difference between 2 sounds of similar frequency
If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats
fbeat = |f1 ndashf2|
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Beats
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Beats and Tuning The beat phenomenon can be used to
tune instruments Compare the instrument to a standard
frequency and adjust so that the frequency of the beats decrease and then disappear
Orchestras generally tune from ldquoArdquo (440 Hz) acquired from the lead oboe or a tuning fork
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
The Doppler Effect
Consider a source of sound (like a car) and a receiver of sound (like you)
If there is any relative motion between the two the frequency of sound detected will differ from the frequency of sound emitted Example the change in frequency of a
carrsquos engine as it passes you
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Stationary Source
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Moving Source
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
How Does the Frequency Change
If the source and the detector are moving closer together the frequency increases The wavelengths are squeezed together and
get smaller so the frequency gets larger
If the source and the detector are moving further apart the frequency decreases The wavelengths are stretched out and get
larger so the frequency gets smaller
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Doppler Effect
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Doppler Effect and Velocity
The degree to which the frequency changes depends on the velocity
The greater the change the larger the velocity This is how police radar and Doppler
weather radar work
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
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
frsquo = v+vD but =vf so
frsquo = f (v+vD v) If the detector is moving away from the
source than the sign is negativefrsquo = f (v vD v)
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Moving Source Stationary Detector
In general = vf but if the source is moving the wavelengths are smaller by vSf
frsquo = v rsquorsquo = vf - vS f
frsquo = v (vf - vSf)
frsquo = f (vv-vS) The the source is moving away from the
detector then the sign is positivefrsquo = f (vv vS)
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
General Doppler Effect We can combine the last two equations and
produce the general Doppler effect formulafrsquo = f ( vplusmnvD vplusmnvS )
What sign should be used Pretend one of the two is fixed in place and determine
if the other is moving towards or away from it For motion toward the sign should be chosen to
increase frsquo For motion away the sign should be chosen to
decrease frsquo Remember that the speed of sound (v) will often be
343 ms
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
The Sound Barrier A moving source of sound will produce
wavefronts that are closer together than normal
The wavefronts get closer and closer together as the source moves faster and faster
At the speed of sound the wavefronts are all pushed together and form a shockwave called the Mach cone
In 1947 Chuck Yeager flew the X-1 faster than the speed of sound (~760 mph) This is dangerous because passing through the
shockwave makes the plane hard to control In 1997 the Thrust SSC broke the sound barrier
on land
Bell X-1
Thrust SSC
Bell X-1
Thrust SSC
Thrust SSC
