If the frequency of sound produced by a siren increases from 400Hz to 1200Hz keeping the amplitude constant. The ratio of the intensity of sound produced at frequency 1200Hz and 400Hz 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 D9:1 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. ⇒I∝f2 So, I1I2=f21f22 ⇒I1I2=120024002=91=9:1 ⇒I1:I2=9:1