A source emitting sound of frequency `165 Hz` is placed in frount of a wall at a distance of `2 m` from it. A detector is also placed in fornt of the wall at the same distance from it. Find the distance between the source and the detector for which the detector detects phase difference of `2pi` between the direct and reflected wave. Speed of sound in air `= 330 m//s`.

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.