Question

$n^{th}$ harmonic of a closed organ pipe is equal to $m^{th}$ harmonic of an open pipe. First overtone frequency of the closed organ pipe is also equal to first overtone frequency of the open organ pipe. Find the value of n if m = 6? ___

Answer 1

$n\left(\frac{V}{4L_C}\right)=m\left(\frac{v}{2L_0}\right)$ ...(i)
$3\left(\frac{V}{4L_C}\right)=2\left(\frac{v}{2L_0}\right)$ ...(ii)
From equation (2), $\frac{L_c}{L_0}=\frac{3}{4}$
From equation (1)
$\frac{n}{m}=2\left(\frac{L_c}{L_0}\right)$
So, n = 9 if m = 6