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Interference, Beats and the Doppler Effect

Lecture 9. Interference, Beats and the Doppler Effect. Pre-reading : §16.6–16.7. 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

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Interference, Beats and the Doppler Effect

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  1. Lecture 9 Interference, Beatsand theDoppler Effect Pre-reading: §16.6–16.7

  2. 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, λ, 2λ, 3λ, ... • Destructive interference (zero amplitude): • path length difference is λ/2, 3λ/2, 5λ/2, ...

  3. 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 ?

  4. Interference in light (non-examinable) • Radio astronomy: interferometers Very Large ArrayNew Mexico, USA Australia Telescope Compact Array, Narrabri, NSW

  5. Young’s double-slit experiment: proof that light is a wave

  6. Precision distance measurement: Gravitational wave detectors The 2-km arms of the LIGO detector in Washington State http://apod.nasa.gov/apod/ap001030.html

  7. Beats • Two (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

  8. 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?

  9. Example: Strobe lighting – 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

  10. Example: Orbital rendezvous

  11. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) Stationary Source Moving Source

  12. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) • Case 1: Source at rest, Listener movingfL = (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 = √[ (c–v) / (c+v) ] × fS c = 3.0 × 108 ms–1

  13. Doppler Effect • Change in perceived frequency due to relative motion of a source (S) and listener (L) • Case 1: Source at rest, Listener movingfL = (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 = √[ (c–v) / (c+v) ] × fS c = 3.0 × 108 ms–1

  14. Next lecture • Doppler effect • and • Shock waves • Read §16.8–16.9

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