  This paper discusses aspects of the second order hyperbolic partial
differential equation associated with the ideal lossless string under tension
and it's relationship to two discrete models. These models are finite
differencing in the time domain and digital waveguide models. It is known from
the theory of partial differential operators that in general one has to expect
the string to accumulate displacement as response to impulsive excitations.
Discrete models should be expected to display comparable behavior. As a result
it is shown that impulsive propagations can be interpreted as the difference of
step functions and hence how the impulsive response can be seen as one case of
the general integrating behavior of the string. Impulsive propagations come
about in situations of time-symmetry whereas step-function occur as a result of
time-asymmetry. The difference between the physical stability of the wave
equation, which allows for unbounded growth in displacement, and computational
stability, that requires bounded growth, is derived.
