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 ure. Suppose the detector is placed at a distance of x meter form the source. The direct wave received from the source travels a siatnce of x meter. Thewave reachign thedetector after reflection from the wall has travelled a distance of `2[(2)^2+x^2/4]^(1/2)` metre. The path difference between the two waves is
`/_\={2[(2)^2+x^2/4]^(1/2)-x}`metre.
constructive interference will take place when `/_\=lamda, 2lamda`....... The minimum distance x for x maximum corresponds to
`/_\=lamda`...... i
The wavelength is `lamda=v/v=(360ms^-1)/(180s^-1)=2m`
Thus `by i 2[(2)^2+x^2/4]^(1/2)-x=2`
or `[4+x^2/4]^(1/2)=1+x/2`
`or, 4+x^2/4=1+x^2/4+x`
`or 3=x`
Thus the detector should be placed at a distance of 3 m from the source. Note that there is no abrupt phase change.