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.

This new notation also introduces a ``
'' superscript to denote a
traveling-wave component propagating to the right, and a ``
''
superscript to denote propagation to the left. This notation is similar to
that used for acoustic tubes [299].