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Question

A point source emits sound of the same power in all directions in a non-absorbing medium. Two points P and Q are at a distance of 9 m and 25 m respectively from the source. The ratio of the amplitude of the waves at P and Q is

A
35
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B
53
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C
925
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D
259
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Solution

The correct option is D 259
We know that the intensity of sound is given by,
I=12ρω2A2ov,
where, ρ is the density of medium, ω is the angular frequency of sound, Ao is the displacement amplitude of particles of medium and v is the speed of sound.
For the same medium and same source of sound,
IA2o
So, I1I2=A2o1A2o2 ..........(1)
Also, we know,
I=PA=P4πr2,
where, P is power, A is surface area and r is distance from the source.
For same power,
I1r2
So, I1I2=r22r21 ..........(2)
From (1) and (2),
Ao1Ao2=r2r1=259

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