Prediction of sound radiation from an unbaffled long enclosure with the ground

Abstract

A theoretical model is presented for the prediction of sound radiated from a semi-infinite unbaffled long enclosure with the ground. This geometrical arrangement forms an idealized representation of traffic tunnels and railway stations where noise propagates inside the long enclosures and radiates to the outside through the openings. Despite the fact that the model described here applies only to idealized situations, it contains essential elements of realistic configurations which are conducive to understanding the physics of the sound radiation phenomenon and significant for the proposal of appropriate noise control strategies. First of all, by expressing the sound field in terms of the superposition of propagating modes inside the long enclosure and adopting the Fourier transform in other regions, the intractable boundary value problem in the natural domain is reduced to a scalar modified Wiener-Hopf (W-H) equation of the second kind in the spectral domain. Then, its solution is obtained using the standard factorization and decomposition procedures, and the radiated sound field is attained through the inverse Fourier transform which involves a contour integral that can be evaluated approximately via the saddle point method. After that, the finite element method (FEM) is adopted to validate the model. Far-field directivity patterns of the radiated sound fields are presented. Finally, the properties of the sound fields both inside and outside three enclosures with different boundary conditions are analyzed, based on which, potential noise reduction methods by using acoustic liners are discussed.