An organ pipe `P_(1)` closed at one end vibrating in its first overtone and another pipe `P_(2)` open at both ends vibrating in third overtone are in resonance with a given tuning fork . The ratio of the length of `P_(1)` to that of `P_(2)` is

Options

A. `3:8`
B. `3:4`
C. `3 :2`
D. `3 : 1`

Answer

a

Explanation

The length of pipe closed at end of the first is
given by
`l_(1) (3l)/4` ...(i)
Length of the pipe open at both end for third ovretone is
given by `l_(2)=(4lambda)/2 = 2lambda` ... (ii)
Dividing Eqs. (i) by (ii), we get
`lambda_(1)/ lambda_(2) = (3lambda//4)/(lambda) = 3/8. `