A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is then the value of a is

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Solution

Q.
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $(\frac{a - 1}{a})$ then the value of $a$ is _________ . [2024]

Ans.
(16) For closed organ pipe

$f_{c} = (2 n + 1) \frac{v}{4 l} = \frac{15 v}{4 l}$

For open organ pipe

$f_{o} = (n + 1) \frac{v}{2 l} = \frac{8 v}{2 l}$

$\frac{f_{c}}{f_{o}} = \frac{15}{16} = \frac{a - 1}{a} \Rightarrow a = 16$

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