Cavities and constrictions in a cylindrical pipe

Let us study what happens when we modify a simple cylindrical pipe by adding a constriction or a widening.

Geometry	Acoustic response	Resonances

In both cases the sudden change in the cross-section of the pipe locally modifies the propagation properties of sound and causes its refraction. The waves meeting the discontinuities are partly reflected and partly transmitted through them, and their amplitude and phase change substantially. Then, in the steady state (that is, after they have travelled back and forth along the pipe several times), they superpose on each other. This interference produces a response of the pipe that differs from the one it would have without the constriction or the widening.

Recall that the acoustic impedance of a pipe is the property describing the relation between the air flow velocity and the resulting acoustic pressure. The smaller the diameter of the pipe, the higher its impedance.

Geometry	Acoustic response	Resonances