When two organ pipes with fundamental frequencies `n_(1) and n_(2)` are connected in series, what will be the resultant fundamental frequency?

Options

A. `(n _(1) + n_(2))`
B. `(n _(2) + n _(2))/( 2)`
C. `sqrt (n_(1) n _(2) + n _(2) ^(2))`
D. `(n _(2)n _(2))/( n _(1) + n _(2))`

Answer

D

Explanation

We have `f = f _(min) = (v)/(2L)`
For open pipe `implies L =(v)/(2f)`
(i) For first pipe. `f _(1) = (v )/( 2L _(1)) = L _(1) = (v)/( 2f _(1))`
(ii) For second pipe, `f _(2) = (v)/( 2L _(2)) implies L _(2) = (v )/(2f _(2))`
Here,` L = L _(1) + L _(2)`
`therefore (v )/( 2f)= (v)/( 2f _(1)) + (v)/( 2f _(2))`
`therefore (1)/(f) = (1)/(f _(1)) + (1)/(f _(2))`
As per the notations used in the equation.
`n = (n _(1) n _(2))/( n _(1) +n_(2))`