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(D) For a closed organ pipe of length $\ell_c$,the fundamental frequency is $f_c = \frac{V}{4\ell_c}$. The first overtone is the third harmonic,so $f_

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$4$:$3$

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(D) For a closed organ pipe of length $\ell_c$,the fundamental frequency is $f_c = \frac{V}{4\ell_c}$. The first overtone is the third harmonic,so $f_{c,1} = 3f_c = \frac{3V}{4\ell_c}$.For an open organ pipe of length $\ell_o$,the fundamental frequency is $f_o = \frac{V}{2\ell_o}$. The first overtone is the second harmonic,so $f_{o,1} = 2f_o = \frac{2V}{2\ell_o} = \frac{V}{\ell_o}$.Given that the frequencies of the first overtones are identical,we have $\frac{3V}{4\ell_c} = \frac{V}{\ell_o}$.Rearranging the terms to find the ratio $\frac{\ell_o}{\ell_c}$,we get $\frac{\ell_o}{\ell_c} = \frac{4}{3}$.

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

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