1 Wave Interference: Beats 2 Beats Previously we considered two interfering waves with the same . Now consider two different frequencies. When waves.

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Presentation transcript:

1 Wave Interference: Beats

2 Beats Previously we considered two interfering waves with the same . 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 beat T

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, v is the speed of wave (343 m/s for sound in air), v s is the speed of the source, f is the frequency of the wave as emitted and f ’ is the detected (Doppler Shifted ) frequency. What do the signs tell us?

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), v D is the speed of the detector, f is the frequency of the wave as emitted and f’ is the detected (Doppler Shifted ) frequency.

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

9 Radar Guns: Detecting Doppler shift Police radar uses electromagnetic waves (v=3x10 8 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.