4.18. Oscillating sphere

In Part XI we derived the radiation impedance for a rigid sphere that oscillates axially. For the results, refer to Eq. (4.137) and Fig. 4.27.
image
Figure 4.33 Exact radiation impedances and admittances for all values of kR for a sphere with a surface that vibrates radially. (a) Mechanical-impedance analogy; (b) acoustic-impedance analogy; (c) mechanical-admittance analogy; (d) acoustic-admittance analogy. The quantity R is the radius of the sphere.
It is seen from Fig. 4.27 that for kR   <   1, that is, when the diameter is less than one-third the wavelength, the impedance load on the surface of the sphere is that of a mass reactance because the resistive component is negligible compared with the reactive component.
At all frequencies, the loading shown in Fig. 4.27 may be represented by the equivalent circuits of Fig. 4.34. The element sizes for the mechanical and acoustic admittances and impedances are given with the circuits.
image
Figure 4.34 Exact radiation impedances and admittances for all values of kR for a rigid sphere that oscillates axially. (a) Mechanical-impedance analogy; (b) acoustic-impedance analogy; (c) mechanical-admittance analogy; (d) acoustic-admittance analogy. The quantity R is the radius of the sphere.
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