Interference, Beats and the Doppler Effect Lecture 9
Pre-reading : 16.616.7
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Wave Interference Two or more traveling waves passing through
same space at same time (identical frequencies) Use principle of
superposition Consider the difference in path length to the sources
Constructive interference (double amplitude): path length
difference is 0, , 2, 3,... Destructive interference (zero
amplitude): path length difference is /2, 3/2, 5/2,...
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Example 16.13 Speakers A and B emit identical sinusoids Speed
of sound is 350 m/s What is frequency of waves if there is
constructive interference at P ? destructive interference at P
?
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Interference in light Australia Telescope Compact Array,
Narrabri, NSW Very Large Array New Mexico, USA 1. Radio astronomy:
interferometers (non-examinable)
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2. Youngs double-slit experiment: proof that light is a
wave
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3. Precision distance measurement: Gravitational wave detectors
http://apod.nasa.gov/apod/ap001030.html The 2-km arms of the LIGO
detector in Washington State
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Beats Two (or more) traveling waves passing through same space
at same time (different frequencies) You hear both frequencies (f a
and f b ) ALSO hear amplitude grow and fall at the beat frequency f
beat = |f a f b | 16.7
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Example One tuning fork vibrates at 440 Hz A second tuning fork
vibrates with unknown frequency With both forks sounded, you hear a
tone with an amplitude that changes with frequency of 3 Hz What is
the frequency of the second tuning fork?
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slowing down a motion Video of a fruit fly using a wing beat
synchronised strobe flash with incrementing phase shift. The motion
is slowed down by a factor of 1:256(The fruit fly beats its wings
200 times a second) https://www.youtube.com/watch?v=Q5rhLHfwpUk
Example: Strobe lighting
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Example: Orbital rendezvous
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Doppler Effect Change in perceived frequency due to relative
motion of a source (S) and listener (L) Stationary SourceMoving
Source
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Doppler Effect Change in perceived frequency due to relative
motion of a source (S) and listener (L) Case 1: Source at rest,
Listener moving f L = (1 + v L /v) f S Case 2: Source and Listener
moving Pay attention to sign of v L, v S ! (positive from L to S)
For light waves f L = [ (cv) / (c+v) ] f S c = 3.0 10 8 ms 1
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Doppler Effect Change in perceived frequency due to relative
motion of a source (S) and listener (L) Case 1: Source at rest,
Listener moving f L = (1 + v L /v) f S Case 2: Source and Listener
moving Pay attention to sign of v L, v S ! (positive from L to S)
For light waves f L = [ (cv) / (c+v) ] f S c = 3.0 10 8 ms 1
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Next lecture Doppler effect and Shock waves Read 16.816.9