## Standing Waves in Pipes

A pipe may be either open or closed.

**Open pipes**

For standing waves in an open open we have antinodes – maximum sound intensity – at both ends.

As a pressure wave travels along the pipe, it may be reflected at at the end. This may seem surprising. It happens because the confining of the air molcules inside the pipe and causes the air inside the pipe to have a different impedance than the air outside. Whenever there is an abrupt change of impedance, such as happens at the open ends, waves are partially reflected.

For the vibrations shown, the wavelengths areIf the speed of sound in air is v, the frequencies will be given by

In general the frequency of the n^{th }harmonic is given by

**Closed Pipes**

Because the pipe is closed at one end, there must be a node at that end. The open end is always a node. This analysis is more complicated. The frequency of the nth harmonic is now (2n-1)f where f is the fundamental frequency and the wavelength of the n^{th} harmonic is