A disk in free space without surrounding structure is a suitable model, at low frequencies, for a direct-radiator loudspeaker without a baffle of any sort. In other words, the loudspeaker radiates as a dipole. The radiation impedance is given by
Eqs. (13.248)–(13.250).
Graphs of the real and imaginary parts of the normalized specific impedance load
on one side of the diaphragm,
Z
s
/
ρ
0
c, as a function of
ka for the free disk, are shown in
Fig. 4.38. The data of
Fig. 4.38 are used in dealing with impedance analogies. For admittance analogies, the complex admittance can be obtained by taking the reciprocal of the complex impedance.
A simple equivalent circuit, approximately valid for all frequencies like those shown in
Fig. 4.37, cannot be drawn for this case. At very low frequencies, however, it is
possible to represent the impedance by an equivalent circuit, which is similar to that for an oscillating sphere. In the frequency ranges where
ka
<
0.5 and
ka
>
5, analogous circuits of the type shown in
Table 4.5 may be used.