Question

Two small loud speakers $A$ and $B$ are driven by the same amplifier as shown in figure and emit pure sinusoidal waves in phase. Speaker $A$ is 1 m away as shown and speaker $B$ is 2 m away from the amplifier. The microphone is 4 m away from the amplifier in transverse direction as indicated in the Figure. For what frequencies destructive interference will occur at $P$ :

• A. 500 HZ, 1500 HZ, 2500 Hz,.....
• B. 500 Hz, 1000 Hz, 1500 Hz,.....
• C. 1250 Hz, 1750 Hz, 2250 Hz,....
• D. 1000 Hz, 2000 Hz.......

Answer 1

The correct option is A 500 HZ, 1500 HZ, 2500 Hz,.....

Path difference between sound from the sources meeting at $P=\sqrt{4^2+2^2}-\sqrt{4^2+1^2}=0.35m$

For destructive interference, path difference=$(n+\frac{1}{2})\lambda =(n+\frac{1}{2})\frac{c}{\nu }$ (n=0,1,2,3...)

$⟹\nu =(n+\frac{1}{2})\frac{350}{0.35}=1000(n+\frac{1}{2})=500Hz,1500Hz,2500Hz....$