Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the…
Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the ratio of the lengths of the pipes.
Solution
Sol. Third overtone of closed organ pipe means seventh harmonic.
Given, $(f_7)_{closed}=(f_4)_{open}$
$7\left(\frac{v}{4l_c}\right)=4\left(\frac{v}{2l_o}\right) \therefore \frac{l_c}{l_o}=\frac{7}{8}$
Answer: $\frac{l_c}{l_o}=\frac{7}{8}$