Question

An organ pipe has two successive harmonics with frequencies 400 and 560 Hz. The speed of sound in air is 344 m/s. What is the length of the pipe in metres?

Answer 1

At any harmonic $n$

$f_1=\frac{nV}{2L}$$=400$ ----eqn. 1

so consecutive harmonic will be $(n+1)$

$f_2=\frac{(n+1)V}{2L}$$=560$ -------eqn. 2

Divide both equation and solve for $n$ , we get

$n=2.5$

Putting it in eqn. 1 and using $V=344m/s$

We get $L=1.075m$