Question

Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the ratio of lengths of the two pipes.

Answer 1

Let `l_(1)=` length of closed organ pipe
`l_(2)=` length of open organ pipe.
Now, frequency of third overtone of closed pipe
`v_(1)=` frequency of 7th harmonic of closed pipe `=7(upsilon//4l_(1))`
and `l_(2)=` frequency of 4the harmonic of open pipe
`=(4 upsilon )/(2l_(2))`
As `v_(1)=v_(2) :. (7 upsilon)/(4l_(1))=(4 upsilon)/(2l_(2))or (l_(1))/(l_(2))=(7)/(8)`