Two speakers connected to the same source of fixed frequency are placed 2.0 m apart in a box. A sensitive microphone placed at a distance of 4.0m from their midpoint along the perpendicular bisector shows maximum response. The box is slowly rotated until the speakers are in line with the microphone. The distance between the midpoint of the speakers and the microphone remains unchanged. Exactly five maximum responses are observed in the microphone in doing this. The wavelength of the sound wave is

Moderate

Solution

Initially S₁M = S₂M
$\Rightarrow$ Path Difference ( $Δ$ x) = $S_{1} M - S_{2} M = 0$

Finally when the box is rotated
Path Difference $= S_{1} M' - S_{2} M' \Rightarrow Δx = 5 - 3 = 2 m$

For maxima
Path Difference = (Even multiple) $\frac{λ}{2} \Rightarrow Δx = (2 n) \frac{λ}{2}$
For 5 maximum responses
$\Rightarrow 2 = 2 (5) \frac{λ}{2} \{∵ Δx = (2 n) \frac{λ}{2}\} \Rightarrow λ = \frac{2}{5} = 0 .4 m$

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