S1 and S2 are two coherent sources of sound of frequency 110Hz 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 330m/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 C3I0 The distance between point 'P' & source S2 is S2P=√32+42=5m
Path difference between waves arriving at 'P' from S1andS2 is, Δx=S2P−S1P=5−4=1m
Phase difference between interferring waves at 'P' will be, Δϕ=KΔx=2πλ×Δx ⇒Δϕ=2π3×1=2π3(∵λ=Vf=330110=3m)
Resultant intensity at 'P' I=I1+I2+2√I1I2cosΔϕ ⇒I=I0+4I0+2√4I20cos(2π3) ⇒I=5I0−2×2I0×12(∵cos2π3=−12) ⇒I=3I0