The Frequency Spectrum of Rectilinearly Moving Point Sources in a Translation-Invariant Environment Applied to Edge Diffraction

In a translation-invariant environment, the three-dimensional sound field can be determined through spatial Fourier transform by superimposing two-dimensional sound fields. This technique is commonly referred to as the 2.5D method, due to the dimensional reduction that takes place. If the sound source is not stationary but moves along the axis of invariance, the calculation of the sound field generally becomes more complex. However, if a harmonically radiating point source moves uniformly at a constant speed along the invariance axis, the opposite is true, and the calculation is significantly simplified. Motivated by the form of the Green’s function in the free field, the so-called separation of variables, or product approach, reduces the problem to a purely two-dimensional one, the general solution of which is referred to in this work as the Product-Doppler formula. Constructing a Fourier integral over the wavenumber domain along the invariance axis is no longer necessary. It is shown that the Product-Doppler formula can be used to solve both interior and exterior problems. The sound field generated by a moving source inside a cylindrical tunnel, and the sound generated by an exterior moving source and scattered from an absorbing cylinder are analyzed. The complex problem of sound diffraction caused by a source moving along the edge of a wedge or a screen is studied in detail. A comparison with results from the literature shows strong agreement.