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

When two organ pipes with fundamental frequencies n_(1)and n_(2) are c

1.	When two organ pipes with fundamental frequencies n_(1)and n_(2) are connected in series, what will be the resultant fundamental frequency?
Answer» `(n _(1) + n_(2))` `(n _(2) + n _(2))/( 2)` `sqrt (n_(1) n _(2) + n _(2) ^(2))` `(n _(2)n _(2))/( n _(1) + n _(2))` SOLUTION :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))`