This letter presents an alternative derivation of the rayleigh integral using the helmholtz equation, indicating new insights on baffled circular pistons.
The study of radiation from baffled circular pistons often begins with the Rayleigh integral. The present letter offers an alternative derivation of the Rayleigh integral by solving the Helmholtz equation for a baffled circular piston in an infinitely large cylindrical waveguide. While the Rayleigh integral is typically interpreted as a sum of simple sources, the present derivation shows that the Rayleigh integral can also be cast as a sum of Bessel beams. The alternative formulation is used to recover the axial pressure radiated by a baffled circular piston and solve the Helmholtz equation numerically for a vortex beam.
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Gokani et al. (2025) studied this question.
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