Question

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 632 Hz . You are standing between the speakers, along the line connecting them and are at a point of constructive interference.How far must you walk toward speaker B to move to reach the first point of destructive interference? (Assume that the speed of sound in air is 344 m/s).

Answer 1

The distance covered by man is 6.4 m

Explanation:

In the interference of two waves , these will fall upon each other .

It will make nodes and anti-nodes in between . There will be one node in between two anti-nodes and  will be one anti-node between two nodes .

The distance between two nodes is λ/2 and distance between two anti-nodes is also λ/2

Thus if the man is at constructive interference , so to move at destructive interference , it has to cover a distance equal to λ/4

Here λ = velocity/frequency = 344/632 = 18.4 m

Thus the distance he will cover = 18.4/4 = 4.6 m