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

$f_{1o} = \frac{v}{L_1 + 2e}$

first overtone of closed organ pipe is given as

$f_{1c} = \frac{3v}{4(L_2 + e)}$

now they are in unison so we will have

$\frac{v}{L_1 + 2e} = \frac{3v}{4(L_2 + e)}$

$\frac{1}{30 + 2e} = \frac{3}{4(23 + e)}$

$90 + 6e = 92 + 4e$

$e = 1 cm$

so end correction of both pipes is e = 1 cm