In this work an accurate analytical solution is found for the sound field in a dome-shaped compression chamber. This simplifies the design and optimization of the compression chamber’s annular exits to suppress high-frequency air resonances. In earlier works by other authors, the solution is also found in spherical coordinates. For low-curvature chambers, an approximation in the form of Bessel function summation was used. For high-curvature compression chambers an analytical approximation did not work and FEA had to be used. The new proposed method is based on Mehler-Dirichlet analytical integral presentation of Legendre functions. This approach handles high-curvature dome chambers and does not require using numerical methods. An evaluation of this new method’s applicability to chambers with various different curvatures was implemented.
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