Audio Engineering

Loudspeakers 683

mass of gas contained in a constriction that is short enough so that all particles are assumed
to move in phase when actuated by a sound pressure. The compliance C of the system is
represented by an enclosed volume, with its associated stiffness. It should be noted that
the mechanical analogue of acoustic compliance is not mechanical stiffness, but rather its
reciprocal, mechanical complianceCm  V s. Although resistance of an acoustic system
may be due to a combination of a number of different factors, irrespective of its origin, it
is conveniently represented by narrow slits in a pipe, for the viscous forces that arise when
gas is forced to fl ow through these slits always results in the dissipation of energy.

The Helmholtz resonator may be graphically represented by Figure 23.6 , but converting it
to its electrical analogue shows it to be a simple resonant circuit, which can be analyzed
easily using general circuit theorems.

M

C

RRRm

C Cm

L m

Inertance Inductance Mass

Compliance Capacitance Compliance

Resistance Resistance Resistance

γ

γ

γ

Figure 23.5 : Acoustical, electrical, and mechanical analogues.

S

R

R

P

M M

C

C P

Figure 23.6 : Schematic representations of a Helmholz resonator.