The acoustic analog of the electrical capacitor or the mechanical spring is a cavity, or a tank (Morse, 1981, p. 234).
In the low-frequency limit, an applied external pressure will compress the enclosed air, which then acts like a spring because of its elasticity. Assuming a cavity volume Q, an increase in applied pressure P will decrease this volume by an amount -dQ.
The ratio of change in volume to original volume is called volume strain or dilation and is given by
For small dilation, Hooke's law for fluids provides an accurate approximation to the relationship between the increase in applied pressure, the resulting strain, and the bulk modulus B,
The bulk modulus for sound waves is nearly adiabatic and is expressed in terms of the density of air and the speed of sound c as
Using Eq. (6) and writing the change in cavity volume, -dQ, in terms of the sinusoidal volume velocity U as
the acoustic impedance of the cavity is given in terms of the Laplace transform by
The impedance of a mechanical spring is equal to k/s, so by analogy the acoustic cavity has an equivalent ``spring constant'' equal to