A handclap on stage in an amphitheater sends out sound waves that scatter from t

Question

A handclap on stage in an amphitheater sends out sound waves that scatter from terraces of width w = 0.988 m (see the figure). The sound returns to the stage as a periodic series of pulses, one from each terrace; the parade of pulses sounds like a played note. (a) Assuming that all the rays in the figure below are horizontal, find the frequency (in Hz) at which the pulses return (that is, the frequency of the perceived note). (b) If the width w of the terraces were smaller, would the frequency be higher or lower (1 denotes higher, 0 denotes lower)? (Note: Assume the speed of sound in air = 343 m/s.)

Explanation / Answer

A)Width of the terraces w=0.75m     Velocity of sound v = 343m/s    (a) If we suppose that a series of pulsesare returning , a pulse which comes back         immedietely afterthe previous pulse will have to travel an additional distance of2w         so, the extratime taken by the pulse,%u0394t=2w/v         and thefrequency of the pulse f=1/%u0394t                                                       = v/2w ..... (1)   (b)From (1) it is clear that the frequency isinversely proportional to width w       so smaller the width ofthe terraces greater would be the frequency.

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