Question

Two coherent point sound sources $S_1$ and $S_2$ are placed as shown in the figure. Both are emitting sound of frequency 165 Hz. $S_1$ is ahead of $S_2$ in phase by $\pi -$radian. (Speed of sound is 330 m/s) How many times maximum sound can be observed on line AB ?

• A. 7
• B. 6
• C. 5
• D. 11

Answer 1

The correct option is B 6

Equation of wave $S_1$ and $S_2$ are

$S_1=Asin(kx-\omega t+\pi )$

$S_2=Asin(kx-\omega t)$

we know $\frac{c}{f}=\lambda =2m$

interference at point A is

$S_1-S_2=Asin(kx-\omega t+\pi )-Asin(kx-\omega t)$

$S_1-S_2=2Asin(\frac{k(x_1+x_2)}{2}-\omega t+\frac{\pi }{2})sin(\frac{k(x_1-x_2)}{2}+\frac{pi}{2})$

$k=\frac{2\pi }{\lambda }=\pi$

hence at point A $x_1=0x_2=8m$

$S_1-S_2=2Asin(4\pi -\omega t+\frac{\pi }{2})sin(-4\pi +\frac{\pi }{2})=2Acos\omega t$

At point A we have a maxima at $t=0$ and after every $2m$ we will get a maxima along AB hence there must 6 maximas.