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Question

If the frequency of sound produced by a siren increases from 400 Hz to 1200 Hz keeping the amplitude constant. The ratio of the intensity of sound produced at frequency 1200 Hz and 400 Hz will be

A
1:1
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B
1:3
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C
3:1
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D
9:1
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Solution

The correct option is D 9:1
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.
I=2π2f2ρA2ov
[ ω=2πf ]
As medium is same and amplitude remain constant.
If2
So,
I1I2=f21f22
I1I2=120024002=91=9:1
I1:I2=9:1

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