An open organ pipe filled with air has a fundamental frequency 500 Hz. The first harmonic of another organ pipe closed at one end and filled with carbon dioxide has the same frequency as that of the first harmonic of the open organ pipe. Calculate the length of each pipe. Assume that the velocity of sound in air and in carbondioxide to be 330 and 264 m/s respectively.

Explanation

To solve this problem, we have to remember that the fundamental mode is itselfthe first harmonic.
`n = (c)/(2l)` for an open pipe
`500 = (300)/(2l) implies l = 30 cm`
`n = (c)/(4l)` for a closed pipe
`500 = (264)/(4l) implies l = 13.2cm`