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Question

A source emitting sound of frequency 180 Hz is placed in front of a wall at a distance of 2 m from it. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = 360 ms−1


A

1 m

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B

2 m

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C

3 m

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D

4 m

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Solution

The correct option is C

3 m


The situation is shown in figure. suppose the detector is placed at a distance of x meter from the source. The direct wave received from the source travels a distance of x meter. The wave reaching the detector after reflection from the wall has travelled a distance of 2 [(2)2+x24]12 meter. The path difference between the two waves is

= { 2[(2)2+x24]12x } meter

Constructive interference will take place when = λ,2λ . . . . . . The minimum distance x for a maximum corresponds to

= λ - - - - - - - - (i)

The wavelength is λ = vf = 360ms1180s1 = 2m

Thus,by (i), 2 [(2)2+x24]12 x = 2

or, [4+x24]12 = 1+x2

or, 4+x24 = 1 + x24+x

or, 3 = x

Thus, the detector should be placed at a distance of 3 m from the source.


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