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A loudspeaker sits in a large room (of length L) against a wall and faces towards...

A loudspeaker sits in a large room (of length L) against a wall and faces towards the opposite wall. The speaker emits a resonant frequency of the room, thus setting up a standing wave. Assume that the wavelength is much smaller than the size of the room, so that the mode number n is high. Use vsnd for the speed of sound.
a.) Your friend starts at the speaker and runs toward the opposite wall at constant speed v. As she does, she hears a loud-soft-loud modulation of the sound intensity. From your perspective, sitting at rest, she is running through nodes and antinodes of the standing wave. Find an expression for the number of sound maxima she hears per second, only in terms of the variables given above.
b.) From your friend’s perspective, the two sound waves are not the same frequency, so they don’t create a standing wave. Find an expression for the beat frequency that she hears, again, only in terms of the variables given above.
c.) Are your answers in (a) and (b) the same, or different? Should they be?

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genius_generous answered 2 years ago
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