1. Radiation from omnidirectional sources

1.1 Radiation impedance of the pulsating sphere

Each surface element dS of a pulsating sphere exerts a force df ₀ on the fluid (figure 1 ).

As in the case of the membrane vibrating at the end of a tube of constant cross-section (see article § 1.4.2), we are led to define, for the sphere vibrating with an effective velocity v _a , a radiation impedance Z _R : $Z_{\text{R}}={\displaystyle \underset{4\text{π}}{\int }\frac{\text{d}{f}_0}{v_a}=4\text{π}{a}^2{Z}_{\text{S}}\left(a\right)}$

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