Surface Pressures Generated by Pistons on Large Spherical and Cylindrical Baffles

The classical solutions for pressures generated by pistons on spheres or infinite strips on cylinders are wave‐harmonic series, which converge poorly for large ka. For pistons on cylinders, the pressures are given by inverse transforms that must be evaluated numerically. The present formulation overcomes these difficulties. Adapting a technique used in antenna studies, the wave‐harmonic series for pistons on spheres and strips on cylinders are transformed into Watson‐Sommerfeld series that converge rapidly except on and near the piston. Here, a Kirchhoff approximation ignoring surface curvature is used. For rectangular pistons on cylinders, analytical integration of the Watson‐Sommerfeld series yields an explicit solution: Wave‐fronts spread circumferentially with the creeping‐wave velocity and axially with the sound velocity, forming elliptical traces on the cylinder. Pressures decay more gradually with axial than with angular separation. For the latter,pressures decay as $θ−12e−Aθ$⁠, as compared to e^−Aθ for strips on cylinders and $(sinθ)−12e−Aθ$ for pistons on spheres.