Two sound sources emitting sound each of wavelength `lambda` are fixed at a given distance apart. A listener moves with a velocity `u` along the line joining the two suorces. The number of beats heard by him per second is

Options

A. `(2u)/(lamda)`
B. `(u)/(lamda)`
C. `(u)/(2lamda)`
D. `(lamda)/(u)`

Answer

A

Explanation

Let n be the original frequency of each source and v be the velocity of sound
The observer at C is approaching the source at A with a speed u. The apparent frequency of A as heard by the listener is `n_(1) = ((v + u)/(v)) n`
But the listener is moving away from B
`:.` The apparent frequency of B as heard by the listener is
`n_(2) = ((v - u)/(v)) n " as " n_(1) gt n_(2)`
`:.` No. of beats `(x) = n_(1) - n_(2)`
`:. x = (n)/(v) [v + u - v + u] = (2n u)/(v)`
But `v = n lamda`
`:. x = (2nu)/(n lamda) = (2u)/(lamda)`