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

PLEASE RATE ME AND AWARD ME KARMA POINTS IF IT IS HELPFUL FOR YOU Given that the two speakers are vibrating out of phase The difference in the path lengths travel by the two sounds is one half a wavelength is f = L_1 - L_2 = ?/2 f = v / ? = v / 2f f = v / 2( L_1 - L_2 ) distances L_1 and L_2 are L_1 = v ( 4.15 m)^2 + ( 3.31/2 + 0.96m)^2 = 4.905 m L_2 = v ( 4.15 m)^2 + ( 3.31/2 - 0.96 m)^2 = 4.23m f = 343 m/s / 2 ( 4.905 - 4.20m) = 486.5 Hz

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