Two closed organ pipes have lengths L and `L+X`. When two pipes are sounded together , the beat frequency is

Options

A. `(vx)/(4L(L+x))`
B. `(vx)/(4L(L-x))`
C. `(4L(L+x))/(vx)`
D. `(2L(L-x))/(vx)`

Answer

A

Explanation

Frequency of vibration in the closed organ pipes are
`v_1=(v)/(4L) and v_2=(v)/(4(L+x))`
`therefore v=v_1-v_2=(v)/(4L)-(v)/(4(L+x))`
`=(v[4(L+x)-4L])/(4Lxx4(L+x))=(vx)/(4L(L+x))`