Question

The fundamental frequency of an open organ pipe is 300 hz.The first overtone of the pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of the closed organ pipe is

Answer 1

Answer: The length of the closed organ pipe is 41.25 cm.

Explanation:

Given that,

Fundamental frequency of an open organ pipe = 300 hz

First overtone of open pipe = $\dfrac{v}{L}$

First overtone of close pipe = $\dfrac{3v}{4L}$

Speed of sound v = 330 m/s

We know that, the fundamental frequency

$f = \dfrac{v}{2l} = 300 hz$

First overtone of open pipe

$\dfrac{v}{L} = 600 hz$

If the first overtone of an open organ pipe = first overtone of a closed organ pipe

$600 = \dfrac{3\times330}{4\times L}$

Therefore, the length of the closed organ pipe

$L = \dfrac{3\times330\ m/s}{4\times 600\ s_{-1}}$

$L = 0.4125\ m$

$L = 41.25\ cm$

Hence, the length of the closed organ pipe is 41.25 cm.