The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end, both of same length, are ' n 1 ' and ' n 2 ' respectively, then

Question

The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end, both of same length, are ' n 1 ​ ' and ' n 2 ​ ' respectively, then

TestHub · Accepted Answer

The fundamental frequency of an air column in a pipe open at both ends is given by $n_{1} = \frac{v}{2 L}$ , where $v$ is the velocity of sound and $L$ is the length of the pipe.

The fundamental frequency of an air column in a pipe closed at one end is given by $n_{2} = \frac{v}{4 L}$ .

Taking the ratio of the two frequencies:

$\frac{n _{1}}{n _{2}} = \frac{\frac{v}{2 L}}{\frac{v}{4 L}} = 2$

$n_{1} = 2 n_{2}$

Answer: $n_{1} = 2 n_{2}$

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