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Q.

Two loudspeakers A and B, 1.0 m apart, produce sound waves of the same wavelength and in the same phase. A sensitive sound detector, moving along P Q parallel to line AB ,2.4 m away, detects maximum sound at P (on the perpendicular bisector of AB) and another maximum sound when it first reaches Q directly opposite to B as shown . The wvelength of sound emitted by the speakers is

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a

0.2m

b

0.8m

c

1.0m

d

0.4m

answer is A.

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Detailed Solution

We know that the path difference between two consecutive maxima = $λ, i. e .$
$A Q - B Q = λ F r o m f i g u r e A Q = \sqrt{[(B Q)^{2} + (A B)^{2}]} = \sqrt{[(2 \cdot 4)^{2} + (1)^{2}]} = 2 \cdot 6 m 2 \cdot 6 - 2 \cdot 4 = λ or λ = 0 \cdot 2 m$

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Two loudspeakers A and B, 1.0 m apart, produce sound waves of the same wavelength and in the same phase. A sensitive sound detector, moving along P Q parallel to line AB ,2.4 m away, detects maximum sound at P (on the perpendicular bisector of AB) and another maximum sound when it first reaches Q directly opposite to B as shown . The wvelength of sound emitted by the speakers is