To carry the traveling-wave solution into the ``digital domain,'' it is necessary to sample the traveling-wave amplitudes at intervals of seconds, corresponding to a sampling rate samples per second. For CD-quality audio, we have kHz. The natural choice of spatial sampling interval is the distance sound propagates in one temporal sampling interval , or meters. In a lossless traveling-wave simulation, the whole wave moves left or right one spatial sample each time sample; hence, lossless simulation requires only digital delay lines. By lumping losses parsimoniously in a real acoustic model, most of the traveling-wave simulation can in fact be lossless even in a practical application.
Formally, sampling is carried out by the change of variables
Substituting into the traveling-wave solution of the wave equation gives