The frequency of the second overtone of an op | vedclass

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(A) For an open pipe of length $L_o$,the frequency of the $n^{th}$ harmonic is $f_n = \frac{n v}{2 L_o}$. The second overtone corresponds to the $3^{r

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(A) For an open pipe of length $L_o$,the frequency of the $n^{th}$ harmonic is $f_n = \frac{n v}{2 L_o}$. The second overtone corresponds to the $3^{rd}$ harmonic $(n=3)$,so $f_{o} = \frac{3 v}{2 L_o}$.For a closed pipe of length $L_c$,the frequency of the $n^{th}$ harmonic is $f_n = \frac{(2n-1) v}{4 L_c}$. The first overtone corresponds to the $3^{rd}$ harmonic $(n=2)$,so $f_{c} = \frac{3 v}{4 L_c}$.Given that $f_o = f_c$,we have $\frac{3 v}{2 L_o} = \frac{3 v}{4 L_c}$.Simplifying this,we get $\frac{1}{2 L_o} = \frac{1}{4 L_c}$,which implies $\frac{L_o}{L_c} = \frac{4}{2} = \frac{2}{1}$.

The frequency of the second overtone of an open pipe is equal to the frequency of the first overtone of a closed pipe. The ratio of the lengths of the open pipe to the closed pipe is

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