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Question

The ratio of intensities between two coherent sound sources is 9:1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is

A
10log4
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B
10log9
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C
10log3
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D
log3
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Solution

The correct option is A 10log4
Given that,
I1I2=91I1I2=3
From formula
ImaxImin=[I1+I2I1I2]2
i.e. ImaxImin=⎢ ⎢ ⎢ ⎢ ⎢I1I2+1I1I21⎥ ⎥ ⎥ ⎥ ⎥2=[3+131]2=(42)2=4

So, sound level for Imax, βmax=10log(ImaxI0)
and βmin=10log(IminI0)
So,
βmaxβmin=10log(ImaxI0)10log(IminI0)
=10log(ImaxI0×I0Imin)
=10log(ImaxImin)=10log4

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