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lecture28 - beats-

# lecture28 - beats- - What you will be able to do a/er today...

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What you will be able to do a/er today … the condi4ons for beats the origin of the ‘so/-­૒loud-­૒so/-­૒ loud’ pulsing of the modulated frequency the average frequency and why it ma?ers Explain … the average frequency and the modulated frequency Calculate … knowledge of traveling wave superposi4on and interference to two waves of slightly different frequencies. CHALLENGE: extend to Doppler effect Apply …

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Noise Cancellation Headphones Based on destructive interference. Work best for constant low- frequency noise. Noise is picked up by microphone, and played back over the headphones in real time but with a phase shift of π . Original noise and played back noise interfere destructively.
Interference in Time: Beats So far: Superposition of waves with same frequency and similar amplitudes. What happens if waves have different frequency? We get a superposition of the two waves as usual but no continual constructive or destructive interference. Why? Two waves with different frequency cannot remain in phase over more than a few cycles. video

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When two waves of slightly different frequencies combine at a point in space (e.g. at your ears) they periodically match up such that their crests (or troughs) coincide. At those instants the resultant amplitude is maximum possible and a maximum in the sound level is heard. As the waves go out of phase they resultant amplitude decreases and the sound level decreases, passing through a minimum (when the crest of one matches up with the trough of the other). The number of times per second the sound level becomes maximum is called the beat frequency The beat frequency is equal to the difference of the two frequencies . Simulation
1 (0, ) sin(10 ) D t t π = 2 (0, ) sin(12 ) D t t π = (0, ) sin(10 ) sin(12 ) D t t t π π = + t

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2 1 beat frequency Beat f f f = = Frequency that you hear = f avg = f 1 + f 2 2 Beat frequency is the number of times one hears a maximum in loudness, PER second.
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lecture28 - beats- - What you will be able to do a/er today...

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