Acoustic directivity ($p\sim r^{-(d-1)/2}\mathcal{D}(\hat{\mathbf{x}})e^{i(k_{0}r-\omega t)}$)

Acoustic directivity describes the angular dependence of radiation in the acoustic far field. For a time-harmonic source in $d$ spatial dimensions, separating the geometric spreading and oscillatory phase leaves a complex amplitude pattern $\mathcal{D}$. The angular intensity pattern is proportional to $|\mathcal{D}{|}^2$. Directivity can be normalized by a reference direction or total radiated power; a stated convention is needed when comparing absolute directivity factors.