A source emitting sound of frequency `180 Hz` is placed in front of a wall at distance of `2 m` from it . A detector is also placed in front of the wall at the same distance from it. From the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air `= 360 m//s`.

Explanation

The situation is shown in figure-6.30.

Suppose the detector is placed at a distance ofj: meter from the source. The direct wave received from the source travels a distance x meter. The wave reaching the detector after reflection rom the wall has travelled adistance of `2[sqrt((2)^(2) + x^(2)//(4))]` meter. Thus the path difference between the two waves at detector is
`Delta= {2sqrt((2)^(2) + (x^(2))/(4) - x)}`
Constructive interference will take place when `Delta = lambda, 2lambda, ... ` Thus the minimum distancesfor which a maximum occurs at detector, the path difference will be
`Delta = lambda`
The wavelength is `lambda = (v)/(n) = (360)/(180)` = 2m
From equation-(6.110) and (6.111), we have
`Delta = 2sqrt(2^(2) + x^(2)/(4)) - x = 2`
`sqrt(4 + x^(2)/(4)) = 1 + (x)/(2)`
`4 + (x^2)/(4) = 1 + (x^2)/(4) + x`
x = 3 m