Operation Manual

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

frequency

Hzf0

cutoff frequency

2f0 3f0 4f0 5f0 6f0

Figure 90: Resonance frequencies of a cylinder with both extremities open.