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Physics - Closed-end pipes

Closed-end pipes

Some musical instruments are more accurately modelled as pipes closed at
one end. The standing waves established in closed end pipes are shown
below. Note that at each open end a pressure node (displacement antinode)
is formed. At any closed end a displacement node (pressure antinode) is
formed. A displacement node must be formed here since the particles in this
region are unable to move due to the closed end.

The fundamental frequency allows one quarter of a full wavelength to fit
inside the length of the pipe. The frequencies of the higher harmonics are
only the odd number multiples of the fundamental frequency. We say that
closed pipes produce only the odd harmonics. Note the relationships between
frequency, wavelength and pipe length.

Two types of diagrams can be presented. You can simply convert from one
form to another using the previously stated idea:

In each case the calculations regarding wavelength, frequency and pipe
length are identical. In an exam you are expected to be able to cope with
either type of diagram.

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