A sound source, detector and a cardboard are arranged as shown in figure. The wave is reflected from the cardboard at the line symmetry of source edetector. Initially the path difference between the reflected wave and the direct wave is one third of the wavelength of sound. Find the minimum distance by which the cardboard should be moved upwards so that both waves are in phase.

Answer

`4 cm`

Explanation

Initially path difference for same phase `2S_(1) - 24 = lambda//3` …..(i)
`rArr lambda = 6`
If shifting is `x` for bring waves in phase `2S_(1) ' -24 = lambda` ……(ii)
subtract `(2)` and `(1)`
`2S_(1) - 2S_(1) = (2lambda)/(3)`
`S_(1) - S_(1) = (lambda)/(3)`
`S_(1) - S_(1) = (6)/(3)`
`sqrt((5 + x)^(2) + 12^(2)) - sqrt(5^(2) + 12) = 2`
on solving `x = 4 cm`