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Question

The intensity level 1 m away from a point source is 40 dB. Threshold intensity of hearing is 1012 W/m2. If there is no loss of power in air, then intensity level at 10 m from the source is

A
30 dB
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B
10 dB
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C
20 dB
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D
40 dB
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Solution

The correct option is C 20 dB
Given that,
I0=1012 W/m2 , r1=1 m , r2=10 m , β1=40 dB

We know that, for a point source,

Intensity (I)1r2

I1I2=(r2r1)2=(101)2=100
So, from the relation between the loudness and intensity of sound, we can write that,

β1=10log10I1I0 and β2=10log10I2I0
β2β1=10log10I2I1

β2=10log10(1100)+40β2=20+40=20 dB

Thus, option (c) is the correct answer.

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