The frequency of the first overtone of a clos | vedclass

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(D) For a closed pipe, the frequency of the $n$-th overtone is given by $f_{c} = \frac{(2n+1)v}{4l_{1}}$, where $n$ is the overtone number. For the fi

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(D) For a closed pipe, the frequency of the $n$-th overtone is given by $f_{c} = \frac{(2n+1)v}{4l_{1}}$, where $n$ is the overtone number. For the first overtone $(n=1)$, $f_{c} = \frac{3v}{4l_{1}}$.For an open pipe, the frequency of the $n$-th overtone is given by $f_{o} = \frac{(n+1)v}{2l_{2}}$, where $n$ is the overtone number. For the first overtone $(n=1)$, $f_{o} = \frac{2v}{2l_{2}} = \frac{v}{l_{2}}$.Given that the frequencies are equal: $\frac{3v}{4l_{1}} = \frac{v}{l_{2}}$.Rearranging for the ratio: $\frac{l_{1}}{l_{2}} = \frac{3}{4}$.

The frequency of the first overtone of a closed pipe of length $l_{1}$ is equal to that of the first overtone of an open pipe of length $l_{2}$. The ratio of their lengths $(l_{1}: l_{2})$ is

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