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Wave Interference: Beats

Wave Interference: Beats. Beats. Previously we considered two interfering waves with the same w . Now consider two different frequencies.

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Wave Interference: Beats

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  1. Wave Interference: Beats

  2. Beats • Previously we considered two interfering waves with the same w. Now consider two different frequencies. When waves of two slightly different frequencies arrive at a point, a detector (ear?) at that point is subjected to two different sinusoidal signals. The superposition of those two signals produces “beats”.

  3. Beat frequency

  4. What we perceive T Tbeat

  5. Doppler (frequency) shift • When the source and receiver are in relative motion, wave fronts get compressed or stretched in time. • Doppler link

  6. Doppler shift for moving source • If the detector and medium are stationary, What do the signs tell us? v is the speed of wave (343 m/s for sound in air), vs is the speed of the source, f is the frequency of the wave as emitted and f ’ is the detected (Doppler Shifted ) frequency.

  7. Doppler shift for moving detector • If the source and medium are stationary, v is the speed of wave (343 m/s for sound in air), vD is the speed of the detector, f is the frequency of the wave as emitted and f’ is the detected (Doppler Shifted ) frequency.

  8. D Toward D Away S Toward S Away Putting source and detector motion into one equation • We can combine these if we measure everything in a fixed medium.

  9. Radar Guns: Detecting Doppler shift • Police radar uses electromagnetic waves (v=3x108 m/s), therefore the relative change in frequency due to reflection from an object travelling (100 m/s) is small. • The best way to detect the difference between the emitted and reflected waves is to add them together in your detector and observe the beats.

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