In many acoustic systems, such as piano strings (§9.4.1,§C.6), wave propagation is also significantly dispersive. A wave-propagation medium is said to be dispersive if the speed of wave propagation is not the same at all frequencies. As a result, a propagating wave shape will ``disperse'' (change shape) as its various frequency components travel at different speeds. Dispersive propagation in one direction can be simulated using a delay line in series with a nonlinear phase filter, as indicated in Fig.2.5. If there is no damping, the filter must be all-pass , i.e., for all .