4.20. Plane circular free disk

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.
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Figure 4.38 Real and imaginary parts of the normalized specific radiation impedance Z s /ρ 0 c of the air load on one side of a plane circular piston of radius a in free space. Frequency is plotted on a normalized scale, where ka   =   2πa/λ   =   2πfa/c.
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