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)/(lambda)`
B. `(u)/(lambda)`
C. `sqrt(u lambda)`
D. `(u)/(2 lambda)`

Answer

A

Explanation

For first source
`n_(1) = n ((v - u)/(v)) = (1 - (u)/(v))n`
for Iind source
`n_(2) = n ((v + u)/(v)) = (1 + (n)/(v)) n`
Beat freq. `= [n_(1) - n_(2)] = n + (nu)/(v) - n + (nu)/(v)`
`= (2nu)/(v) = 2 (u)/(lambda) [:' v = n lambda :. (1)/(lambda) = (n)/(v)]`