Analysis of acoustic directivity of spherical cap transducers

In order to study the acoustic radiation from the spherical cap transducer,a theoretical model is used by solving the wave equation in spherical coordinates using the method of separation of variables,based on the spherical harmonic Fourier transform and boundary condition.The calculation formulas for the far field radiated pressure and directivity of spherical cap are derived.Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angles of the spherical cap,radii of sphere baffle and operating frequencies.Both the diameter of the sphere baffle and the wavelength determine the directivity of acoustic radiation from a spherical cap.When the frequency is lower or the wavelength is longer than the diameter of the sphere baffle,the acoustic radiation from a spherical cap is omnidirectional.With the increase of the frequency or the diameter of the sphere baffle,the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle.Furthermore,the ripple in the beam is more obvious.The high frequency spherical cap transducer was fabricated and the directivity pattern was tested and the measurement data is shown to coincide with the theoretical results.This research can provide a guideline for designing the spherical cap transducers and arrays.