The intensity level 1m away from a point source is 40dB. Threshold intensity of hearing is 10−12W/m2. If there is no loss of power in air, then intensity level at 10m from the source is
A
30dB
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B
10dB
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C
20dB
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D
40dB
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Solution
The correct option is C20dB Given that, I0=10−12W/m2,r1=1m,r2=10m,β1=40dB
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 ⇒β2−β1=10log10I2I1