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 = 0.91 m (see the figure below). 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 are horizontal, find the frequency 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?

Explanation / Answer

That's a strange question! Consider that
v = 343 m/s = f?
I think that we have to assume that
? = 2w = 1.82 m, since when the first wave reflects, the second wave travels out w before reflecting, while the first wave has traveled in w.
Therefore f = 343m/s / 1.82m = 188 Hz

b) If the terraces are smaller, ? is smaller, so the frequency is larger (higher).

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