The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is.

Question

The frequency of the second overtone of the pipe is equal to the frequency of the first overtone of the closed pipe- The ratio of the lengths of the pipe and the closed pipe is-1-31-22-13-1

Toppr Admin · Accepted Answer

Let the lengths of open pipe and closed pipe be $L$ and $l$ , respectively.
Frequency of second overtone (or third harmonic i.e $n = 3$ ) of open pipe $ν = \frac{n v}{2 L} = \frac{3 v}{2 L}$

Frequency of first overtone (or third harmonic ie. $m = 2$ ) of open pipe $ν^{'} = \frac{(2 m - 1) v}{4 l} = \frac{3 v}{4 l}$
But $ν = ν^{'}$
$∴$ $\frac{3 v}{2 L}$ $= \frac{3 v}{4 l}$ $⟹ L : l = 2 : 1$

The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is.1:31:22:13:1

Let the lengths of open pipe and closed pipe be L and l, respectively.Frequency of second overtone (or third harmonic i.e n=3) of open pipe ν=nv2L=3v2LFrequency of first overtone (or third harmonic ie. m=2) of open pipe ν′=(2m−1)v4l=3v4lBut ν=ν′∴ 3v2L=3v4l ⟹L:l=2:1

The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is.
$1 : 3$
$1 : 2$
$2 : 1$
$3 : 1$