Question

Two small loud speakers $A$ and $B$ are driven by the same amplifier as shown in Fig 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 constructive interference will occur at $P$ (microphone point) :

• A. 1000 Hz,2000 Hz, ........
• B. 500 Hz, 1500 Hz ........
• C. 550 Hz, 1100 Hz.........
• D. 500 Hz, 1000 Hz,1500 Hz,.......

Answer 1

The correct option is A 1000 Hz,2000 Hz, ........

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

For constructive interference, path difference $=$ $n\lambda =n\frac{c}{\nu }$

$⟹\nu =\frac{nc}{0.35}=\frac{n\left(350\right)}{0.35}=1000n=1000Hz,2000Hz,3000Hz....$