Sound from coherent sources `S_(1) and S_(2)` are sent in phase and detected at point `P` equidistant from both the sources . Speed of sound in normal air in `V_(0)`, but in some part in path `S_(1)` , there is a zone of hot air having temperature ` 4 times` , the normal temperature , and width `d`. What should be minimum frequency of sound , so that minima can be found at `P`?

Answer

`f_(max) = (V)/(d)`

Explanation

Path differnce `= (mu - 1)d`
`mu = (V_(0))/(V') = (sqrt((gamma R(T_(0)))/(m_(0))))/(sqrt(( gamma R ( 4 T_(0)))/(m_(0)))) = (1)/(2)`
(i) `| path differnce | = |(1/2 - 1)d | = (d)/(2)`
For minima , path difference ` = ( 2 n + 1) (lambda)/(2) = (d)/(2)`
`(d)/(( 2n + 1)) = lambda = (V)/(f)`
`f = (V ( 2n + 1))/( d)`
`f_(min) = (V)/(d)`