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 = 360 ms−1
3 m
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+x24]12 meter. The path difference between the two waves is
△ = { 2[(2)2+x24]12−x } meter
Constructive interference will take place when △ = λ,2λ . . . . . . The minimum distance x for a maximum corresponds to
△ = λ - - - - - - - - (i)
The wavelength is λ = vf = 360ms−1180s−1 = 2m
Thus,by (i), 2 [(2)2+x24]12 − x = 2
or, [4+x24]12 = 1+x2
or, 4+x24 = 1 + x24+x
or, 3 = x
Thus, the detector should be placed at a distance of 3 m from the source.