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Question

# A point source emits sound waves of constant power with intensity inversely proportional to the square of the distance from the source. By how many decibels does the sound loudness drop, when you move from point A to B ? Distance of B from the source is two times the distance of A from the source. [Take log102=0.3 ]

A
4 dB
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B
2 dB
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C
6 dB
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D
8 dB
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Solution

## The correct option is C 6 dBWe know that for a point source, Intensity I∝1r2 From the data given in the question, IBIA=(rArB)2=(12)2=14 ⇒IA=4IB From the relation between loudness and intensity of a sound wave, β=10logII0 We can write that, βB−βA=10logIBI0−10logIAI0 ⇒βB−βA=10log[IBI0×I0IA]=10log(IBIA) ⇒βB−βA=10log(14) =10×(−2log102)=10×−0.6=−6 dB i.e loudness drops by 6 dB Thus, option (c) is the correct answer.

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