Two organ pipe , both closed at one end , have lengths `l and l + Delta l`. Neglect end corrections. If the velocity of sound in air is `V`, then the number of beats//s` is

Options

A. `(V)/( 4l)`
B. `(V)/( 2l)`
C. `(V)/( 4l^(2)) Delta l`
D. `(V)/( 2 l^(2)) Delta l`

Answer

C

Explanation

`Beats = (V)/( 4 l) - (V)/( 4( l + Delta l)) = (V)/(4) [ ( Delta l)/( l ( l + Delta l))]`
` = (V Delta l)/( 4 l^(2))` `( because Delta l lt lt l)`