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Question

S1 and S2 are two coherent sources of sound of frequency 110 Hz each and have no initial phase difference. The intensity at a point P due to S1 is I0 and due to S2 is 4I0. If the velocity of sound is 330 m/s, then the resultant intensity at P is



A
I0
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B
9I0
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C
3I0
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D
8I0
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Solution

The correct option is C 3I0
The distance between point 'P' & source S2 is S2 P=32+42=5 m
Path difference between waves arriving at 'P' from S1 and S2 is,
Δx=S2PS1P=54=1 m
Phase difference between interferring waves at 'P' will be,
Δ ϕ=KΔ x=2πλ×Δ x
Δ ϕ=2π3×1=2π3(λ=Vf=330110=3 m)
Resultant intensity at 'P'
I=I1 +I2+2I1I2cosΔ ϕ
I=I0+4I0+24I20cos(2π3) 
I=5I02×2I0×12(cos2π3=12)
I=3I0

Physics

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