Two small loudspeakers are connected to a single source—an 888 Hz sine-wave gene

Question

Two small loudspeakers are connected to a single source—an 888 Hz sine-wave generator—so that they are coherent. Suppose that initially the speakers are side by side, a few centimeters apart, equidistant from a listener 2.04 m in front of the speakers.
(a) One of the speakers is slowly moved straight back away from the listener until at some point she hears almost no sound. How far is the speaker moved?
(b) How much farther back should the speaker be moved for the sound to be about as loud as it was initially?

Explanation / Answer

f = c (speed of the wave in m/s)
= Wavelength in meters
f = frequency in Hz

Assuming a speed of sound of 343 m/s (it is temperature dependen)
= 343 / 888 = 0.386 meter

at 2.04 m, the listener is 5.07 wavelengths from the speaker.
Moving the one back by half a wavelength, 0.215 m, will mean the two waves will arrive at the listener out of phase, and therefor partially cancel.

b) another half wave length, 0.215 m

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