Interference, Beats and the Doppler Effect

Interference, Beatsand theDoppler EffectLecture 9Pre-reading: 16.616.7Wave InterferenceTwo or more traveling waves passing through same space at same time (identical frequencies)Use principle of superpositionConsider the difference in path length to the sourcesConstructive interference (double amplitude):path length difference is 0, , 2, 3, ...Destructive interference (zero amplitude):path length difference is /2, 3/2, 5/2, ...Example 16.13Speakers A and B emit identical sinusoidsSpeed of sound is 350 m/sWhat is frequency of waves if there isconstructive interference at P ?destructive interference at P ?

Interference in light

Australia Telescope Compact Array, Narrabri, NSWVery Large ArrayNew Mexico, USA Radio astronomy: interferometers(non-examinable)

Youngs double-slit experiment: proof that light is a wave Precision distance measurement: Gravitational wave detectors

http://apod.nasa.gov/apod/ap001030.htmlThe 2-km arms of the LIGO detector in Washington StateBeatsTwo (or more) traveling waves passing through same space at same time (different frequencies)You hear both frequencies (fa and fb)ALSO hear amplitude grow and fall at the beat frequency

fbeat = |fa fb| 16.7

ExampleOne tuning fork vibrates at 440 HzA second tuning fork vibrates with unknown frequencyWith both forks sounded, you hear a tone with an amplitude that changes with frequency of 3 HzWhat is the frequency of the second tuning fork? 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=Q5rhLHfwpUkExample: Strobe lighting

Example: Orbital rendezvoushttp://www-mgcm.arc.nasa/govmars.jpl.nasa.gov/allaboutmars/extreme/martianyear/Doppler EffectChange in perceived frequency due to relative motion of a source (S) and listener (L)Stationary SourceMoving Source

Doppler EffectChange in perceived frequency due to relative motion of a source (S) and listener (L)Case 1: Source at rest, Listener moving fL = (1 + vL/v) fS Case 2: Source and Listener moving

Pay attention to sign of vL, vS ! (positive from L to S)For light wavesfL = [ (cv) / (c+v) ] fS c = 3.0 108 ms1

Doppler EffectChange in perceived frequency due to relative motion of a source (S) and listener (L)Case 1: Source at rest, Listener moving fL = (1 + vL/v) fS Case 2: Source and Listener moving

Pay attention to sign of vL, vS ! (positive from L to S)For light wavesfL = [ (cv) / (c+v) ] fS c = 3.0 108 ms1

Next lectureDoppler effectandShock waves

Read 16.816.9