An open organ pipe of length l is sounded together with another open organ pipe of length l + x in their fundamental tones. Speed of sound in air is v. the beat frequency heard will be (`x lt lt l`)

Options

A. `( vx)/( 4 l^(2))`
B. `(vl^(2))/( 2x)`
C. `( v x)/( 2 l^(2))`
D. `( v x^(2))/( 2l)`

Answer

C

Explanation

Beat frequency `= f_(1) - f_(2) = (v)/(2 l) - (v)/( 2( l + x))`
` = (v)/( 2 l) [ 1 - ( 1 + (x)/(l))^(-1)]`
` = (v)/( 2l) [ 1 - 1 + (x)/(l)]`
`= ( vx)/( 2l^(2))`