Conical bores. Part II: Multiconvolution

The input impulse response, or related functions such as the plane‐wave or spherical‐wave reflection functions, of a conical bore with discontinuities can be calculated from the reflection functions associated with discontinuities by means of a multiconvolution process. This approach, as alternative to the Fourier transform of the acoustical impedance Z(f), is attractive because of the detailed description it gives of the pressure time evolution inside the bore. However, the calculation may become rather involved if each reflected and transmitted wave is followed individually, and numerical instability may arise whenever the implied reflection functions contain growing exponentials. The first difficulty has been overcome by summing up all outward traveling waves and all inward traveling waves to give a unique outward wave and a unique inward wave. Numerical instability has been avoided by using an iterative convolution algorithm. Internal damping due to viscous and thermal losses has been located at disco...