Two sources `S_1` and `S_2` of same frequency `f` emits sound. The sources are moving as shown with speed `u` each. A stationary observer hears that sound. The beat frequency is (`v=`velocity sound)

Options

A. `(2u^2f)/(v^2-u^2)`
B. `(2v^2f)/(v^2-u^2)`
C. `(2uvf)/(v^2-u^2)`
D. `(2u)/(v)f`

Answer

C

Explanation

Apparent frequency of `S_1` and `S_2` heard by observer is `f_1=(v)/(v-u)f` and `f_2=(v)/(v+u)f`
`:.` Beat `=f_1-f_2=(2uv)/(v^2-u^2)f`