An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

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Aicharya · Accepted Answer

$\frac{\ell_{0}}{\ell_{c}}=?$ $\begin{array}{ll}	ext { For closed pipe } & n_{p}=n_{0}(2 p+1) \Rightarrow n_{l c}=n_{o}^{3} \ 	ext { For open pipe } & n_{p}=n_{0}(p+1) \Rightarrow n_{l o}=n_{0}^{2}\end{array}$ $\begin{aligned} & n_{1 c}=3 n_{0}=\frac{3 V}{4 \ell_{c}} \ & n_{10}=2 n_{0}=\frac{2 V}{2 \ell_{0}} \ 	herefore & \frac{3 V}{4 \ell_{c}}=\frac{2 V}{2 \ell_{0}} \ 	herefore & \frac{\ell_{0}}{\ell_{c}}=\frac{4}{3} \end{aligned}$

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio…

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