A classroom has two speakers. One is mounted to the wall 3m above the floor. The

Question

A classroom has two speakers. One is mounted to the wall 3m above the floor. The other has fallen from its mount, and now sits on a table against the wall, 1 m above the floor and separated from the other speaker by a horizontal distance of 3m. You sit in a desk halfway between the two speakers and 4m from the wall. Your car is 1 m above the floor. If the sound from the speakers is initially in phase, What is the phase difference that you notice when the sound arrives at your ear? What is lowest frequency that you don't hear (i.e. for which there is complete destructive interference)?

Explanation / Answer

a) the distance between your ear and the first speaker is SQRT{(3-1)^2 + 1.5^2 + 4^2}m = 4.71m the distance between your ear and the second speaker is SQRT{(1-1)^2 + 1.5^2 + 4^2}m = 4.27m The difference in phase would be 4.71m - 4.27m = 0.44m. Usually we would give this as a fraction of the wavelength in radians (so that it wouldn't have units) but we don't have a wavelength. b) Destructive interference occurs when the sound is off by half a wavelength or an integer and a half number of wavelenghts. The wavelength is largest when 0.44m is a half wavelength. When the wavelength is maximized, the frequency is minimized. Wavelength = speed/frequency speed of sound at room temp = 343 m/s frequency = speed/wavelength = (343m/s)/0.88m = 386 Hz

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