Doppler Effect
Beats: two waves of almost the same frequency are added.
• Frequency shift when sound source and/or listener is
moving
Amplitude
Sound: Beats, Doppler Effect, Sonic Boom
• When source is moving towards listener pitch appears
_________
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
• When source is moving away from listener, pitch
appears _________
• Example: NASCAR race car passing you
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (sec)
Sign Convention: + from listener to source
Beat frequency:
Demo: Doppler Rocket
Demonstration of Beats
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Doppler Case A:
Moving Source
+
Listener
=0
During one period, Τ, source moves
Wavelength is increased by:
S
=
+
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Example: Tuba on a Train
Source
In one of the original Doppler experiments, a tuba
was played on a moving flat car at 75 Hz. An
identical tuba was played at the train station. The
train approached the station at 12 m/s.
What beat frequency was heard at the train station?
=
=
S
Wave speed remains unaffected; apparent frequency becomes:
= speed of sound; always positive
= =
With source moving towards listener, frequency ________.
With source moving away, frequency __________.
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Doppler Case B:
Moving Listener
+
Listener
Relative velocity:
Tuba at the train station
Source
=0
You are now riding on the flat car moving at 12
m/s and with the tuba playing at 75 Hz. An
identical tuba was played at the train station.
What beat frequency do you hear?
vwave / L = vwave / gr − vL / gr
Wavelength remains the same, so the modified frequency is:
=
=
=
When listener moves towards the source, the frequency __________.
When listener moves away from the source, the frequency ________.
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Hites II, 2013 Lecture 4
Doppler Case C: Moving Source and Listener
Police Car
Moving source: Wavelength changes, but not wave speed
Moving listener: Wave speed changes, but not wavelength
A police car is sounding a siren with 1260 Hz
on a 20°C day. (vsound = 767mph)
 v + vL 

f ′ = f 0 
v
v
+
S 

Police car chasing you.
Frequency of siren:
A: + vL, + vS
B: + vL, - vS
C: - vL, + vS
D: - vL, - vS
Listener
+
The police car is traveling at 70 mph. You are
traveling at 60 mph in the same direction.
What frequency do you hear as the police car
approaches you from behind? (Hz)
Source
Other cases:
• You are chasing police car
• Police car is coming other
way towards you.
The police car is traveling at 70 mph. You are traveling at
60 mph in the same direction. What frequency do you
hear after the police car passes you? (Hz)
• Police car going other way,
passed you.
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Example: Speed of a car
Doppler Applications
A 5000 Hz sound wave is emitted by a stationary source. The
sound wave reflects off a car moving at 60 mph towards the
source. What frequency will be detected by a detector near
the source.
Weather radar: Developed in 1988,
the Doppler shift is used to determine
how fast a storm is moving.
Echocardiography: Ultrasound and
Doppler technology are used to
visualize the structure of the heart.
Areas of the heart that have a high
and low blood velocity can be seen in
different hues of the resulting picture.
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Sonic Booms
• Source of waves moves faster than
the wave speed
• Source is “outrunning” the waves
• Waves pile up along the side
• Crests overlap and form one very
large crest
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