Two sources of sound, ` S_1 and S_2` , emitting waves of equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to `S_1S_2 and at a distance of 20.0 cm from P it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through wffich the detector should be shifted to detect a minimum of sound.

Answer

A, B, C

Explanation

According to the data `lamda=20 cm`
`S_1S_2=20cm`
`BD=20cm`
(Let the detector is shifted to left for a distance x for hearing the minium sound)
so path difference
`sqrt(AB^2+BC-AB)`
`=sqrt((20)^2+(10+x)^2)-sqrt((20)^2+(10-x)^2)`
so the minimum distance hearing for minimum
`=((2n+1)lamda)/2=lamda/2`
`=20/2=10cm`
`rarr sqrt((20)^2+(10+x)^2)=sqrt((20)^2(10-x)^2)=10`
Solving we get x=12.0cm