Q.

As shown in the fig two loudspeakers are located at point A and B. Both are vibrating in phase at a frequency ν and P1 and P2 are their respective power. Point C lies on a line joining two loudspeakers at a distance of d1 from A and d2 from B. When both the speakers are switched on, what is the intensity (in W/m2) at point C? Take velocity of sound 300 ms1, frequency ν =100Hz, d1=1 m and d2= 1.5 m, p1=8π W and p2=18π W. Also assume that loudspeakers behave like isotropic point sources: (emit sound uniformly in all directions)

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a

6W/m2

b

9W/m2

c

12W/m2

d

15W/m2

answer is A.

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Detailed Solution

I1=P14πd12=8π4π×1=2W/m2I2=P24πd22=18π4π×(1.5)2=2W/m2

Path difference  

Δx=d2d1=0.5    =2πλΔx=2π.vVΔx   =2π×100300.12=π3

resulting intensity will be given by 

I=I1+I2+2I1I2cosθ=2+2+22×2cos60=6W/m2

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As shown in the fig two loudspeakers are located at point A and B. Both are vibrating in phase at a frequency ν and P1 and P2 are their respective power. Point C lies on a line joining two loudspeakers at a distance of d1 from A and d2 from B. When both the speakers are switched on, what is the intensity (in W/m2) at point C? Take velocity of sound 300 ms−1, frequency ν =100Hz, d1=1 m and d2= 1.5 m, p1=8π W and p2=18π W. Also assume that loudspeakers behave like isotropic point sources: (emit sound uniformly in all directions)