`n_1 " and " n_2` are the fundamental frequency of two open pipes of same diameter . If these two are joined end to end to form as single pipe, the fundamental frequency of the new pipe formed is

Options

A. `n_1 +n_2`
B. `(n_1+n_2)/(2)`
C. `(n_1n_2)/(n_1+n_2)`
D. `(n_1+n_2)/(n_1n_2)`

Answer

C

Explanation

`n_1=(v)/(1l_1) therefore l_1=(v)/(2n_1)`
`n_2 = (v)/(2l_2) therefore l_2 = (v)/(2n_2)`
`n=(v)/(2l) therefore l=(v)/(2n)`
`l=l_1+l+2`
`(v)/(2n) = (v)/(2n_1) +(v)/(2n_2)`
`1/n = 1/n_1 + 1/n_2`
`1/n = (n_2+n_1)/(n_1n_2)`
`n=(n_1n_2)/(n_1+n_2)`