A source emitting sound of frequency 180 Hz is placed in front of a wall at a distance of 2 m from it. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air `=360ms^-1`.

Explanation

The situation is shown in figure. Suppose the detector is placed at a distance of `x` meter from the source. The direct wave received from the source travels a distance of `x` meter. The wave reaching the detector after reflection from the wall has travelled a distance of `2[(2)^(2) + x^(2)//4]^(1//2)` meter. The path difference between the two waves is
`Delta = {2[(2)^(2) + (x^(2))/(4)]^(1//2)-x} meter`.
`Delta = lambda` for `Deltaphi = 2pi ...(i)`
Thus, by `(i) 2 [(12)^(2) + (x^(2))/(4)]^(1//2) -x = 2`
or, `[4 xx (x^(2))/(2)]` or, `4 + (x^(2))/(4) = 1 + (x^(2))/(4) + x`
or, `x = 3`
Thus, the dector should be placed at a distance of `3m` from the source, Note that there is no abrupt phase change.