A listener is standing in front of two speakers that are producing sound of the

Question

A listener is standing in front of two speakers that are producing sound of the same frequency and amplitude, except that they are vibrating out of phase. Initially, the distance between the listener and each speaker is the same (see the drawing). As the listener moves sideways, the sound intensity gradually increases. When the distance x in the drawing is 0.98 m, the change reaches the maximum amount (from soft to loud). Using the data shown in the drawing and 343 m/s for the speed of sound, determine the frequency of the sound coming from the speakers.

Explanation / Answer

Distance to left speaker after moving sideways = sqrt. (4^2 + (1.5 + 0.98)^2, =4.706 metres.
Distance to right speaker after move = sqrt. (4^2 + (1.5 - 0.98)^2, = 4.0336 metres.
Difference in path lengths = (4.706 - 4.0336), = 0.6724m.
Double this, = 1 wavelength of the sound, = 1.3448 metres.
Frequency = (velocity/ wavelength), =255.056Hz.

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