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6.90 Tube 148
6.90 Tube
The Tube module simulates sound propagation in a cylindrical tube of a given
length and radius. The effect of a tube is to color an input signal by enhancing
frequencies located around its resonance frequencies. When the tube is very long, it
produces an echo effect. The source is assumed to be at an extremity of the tube. The
output of this module is the signal that would be measured by a microphone placed
at the other extremity of the tube. The geometry of the tube is determined during
construction.
Tuning a tube
The resonance frequencies of a tube depend on its length and termination. A tube
with open extremities has resonances located at harmonic intervals, i.e. located at 1, 2, 3 . . . times
any fundamental frequency as can be see in Figure 90. When an extremity is closed, the tube only
has resonance for odd harmonics of its fundamental frequency.
A tube can be tuned by adjusting its length in order to obtain a given fundamental resonance
frequency. When the tube is open at both of its extremities, the fundamental frequency is given by
c/2length where c is the speed of sound (approximately 344 m/s in air, depending on the tempera-
ture) and length is the tube length. For a tube with one extremity closed, the fundamental frequency
is given by c/4length.
amp
dB
frequency
Hzf0
cutoff frequency
2f0 3f0 4f0 5f0 6f0
Figure 90: Resonance frequencies of a cylinder with both extremities open.
148


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