= Point-force radiation from a fluid-loaded sheet
{title2=$\widehat p_+=-F\rho_0\omega^2e^{-\gamma y}/\Delta$}
A harmonic line <force> localized at one point of a two-dimensional sheet gives $\widehat\eta=F/D$ and $\Delta=\gamma D$ in the <Fourier transform>. The outgoing upper <pressure> is the displayed amplitude. Dividing by $c_0^2$ converts it to <acoustic density perturbation>. The <method of steepest descent> gives cylindrical sound from the <saddle point>, while crossed zeros of the <dispersion relation> give guided or leaky modal residues. Retaining $k_0=\omega/c_0$ is essential for dimensionally consistent spreading and prefactors.
Back to article page
