Question

An open organ pipe 30 cm long and a closed organ pipe 23 cm long, both of same diameter , are each sounding its first overtone , and these are in unison. What is the end correction of these pipes?

Answer 1

First overtone of open organ pipe is given as

`f_(1o) = (v)/(L_1 + 2e)`

first overtone of closed organ pipe is given as

`f_(1c) = (3v)/(4(L_2 + e))`

now they are in unison so we will have

`(v)/(L_1 + 2e) = (3v)/(4(L_2 + e))`

`(1)/(30 + 2e) = (3)/(4(23 + e))`

`90 + 6e = 92 + 4e`

`e = 1 cm`

so end correction of both pipes is e = 1 cm