In the figure shown S1 and S2 are two identical coherent sources of sound, separated by d. A receiver moves along line XY which is parallel to S1S2 to detect intensity of sound at various points on the line. Distance of line XY from S1S2 is D (D>>d). Distance of first intensity maxima on line XY measured from O is y. Find percentage change in value of y if the temperature of air increases by 1%. If your answer is X% fill value of 6X.

y=Dd1frRTMy∝TΔyy=12ΔTTΔyy×100=12×1% change in y=12

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In the figure shown S₁ and S₂ are two identical coherent sources of sound, separated by d. A receiver moves along line XY which is parallel to S₁S₂ to detect intensity of sound at various points on the line. Distance of line XY from S₁S₂ is D (D>>d). Distance of first intensity maxima on line XY measured from O is y. Find percentage change in value of y if the temperature of air increases by 1%. If your answer is X% fill value of 6X.

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answer is 3.

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Detailed Solution

$\begin{array}{l} y = \frac{D}{d} (\frac{1}{f} \sqrt{\frac{rRT}{M}}) \\ y \propto \sqrt{T} \\ \frac{Δy}{y} = \frac{1}{2} \frac{ΔT}{T} \\ \frac{Δy}{y} \times 100 = \frac{1}{2} \times 1 \end{array}$
$% change in y = \frac{1}{2}$

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