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Two speakeer connected to the same sourc...

Two speakeer connected to the same source of fixed frequency are placed 2m apart in a box. A sensitive microphone placed at a distance of 4m from the midpoint alon the perpendicular bisector shown maximum response. The box is slowly rotated till the speaker are in line with the microphone, The distance between the midpoint of the speakers and the microphone remains unchanged. Exactly 5 maximum responses (inculuding the initial and last one) and observed in the microphone in doing this. The wavelength of the sound wave is (o.x) meter. Find the value of x.

Text Solution

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The initial and final positions of speakers ` S_(1) and S_(2)` and microphone `M` are shown in Figs. S7.2 (a) and (b). Intially the path difference from `S_(1) to M and S_(2) to M` is zero .
I.e. `S_(2) M - S_(1) M = 0`
Finally the path difference
`Delta = S_(2)P - S_(1)P = 5 - 3 = 2 m`
For `n th "maxima" Delta = n lambda`
` 2 = 5 lambda or lambda = 2//5 = 0.4 m`
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