Question

Three sources of sound $S_1,S_2$ and $S_3$ of equal intensity are placed in a straight line with $S_1{S}_2=S_2{S}_3$(figure). At a point P, far away from the sources, the wave coming from $S_2$ is ${120}^o$ ahead in phase of that from $S_1$. Also, the wave combing from $S_3$ is ${120}^o$ ahead of that from $S_2$. What would be the resultant intensity of sound at P?

Answer 1

Let S be the amplitude of the sound sources from $S_1,S_2,S_3$

$I_{\sec }=I_1=I_2+I_3$

$S\left(cos\right(\theta -{120}^o)cos\theta +s\cos (\theta +{120}^o\left)\right)$

$=S(\cos \theta +\cos (\theta -{120}^o)+\cos (\theta +{120}^o\left)\right)$

$=S(\cos \theta +2\cos \theta \cos (-{120}^o\left)\right)$

$=S(\cos \theta +2\cos \theta =\frac{-1}{2})$

$=S(\cos \theta -\cos \theta )$

$=0$