### An Acoustic Mass (Inertance)

• In the low-frequency limit, the air within a short, open tube will be displaced by equal amounts at both its ends when subjected to an external pressure at one end only. If the length and cross section of the tube are given by L and A, respectively, then the enclosed air has a mass of , where is the mass density of air.

• The acoustic response of this system is analyzed by assuming an applied sinusoidal pressure of the form . Using Newton's second law (force = mass x acceleration),
 (3)

where is the acoustic volume velocity of the air mass.

• The volume velocity response to the applied pressure will also vary sinusoidally with frequency so that Eq. (3) reduces to
 (4)

• The acoustic impedance of the tube is then given by
 (5)

(or when expressed in terms of the Laplace transform), where initial conditions are assumed equal to zero.

• In the low-frequency limit, the open tube is called an acoustic inductance or an inertance and it has a direct analogy to the inductance in electrical circuit analysis or the mass in mechanical system analysis.

• The impedance of a mechanical mass is equal to m s, and thus the open tube has an equivalent acoustic mass'' equal to An inertance is also sometimes referred to as a constriction (Morse, 1981, p. 234).