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