The Ideal Struck String

• An ideal struck string involves zero initial displacement and a nonzero initial velocity distribution.

• The simulation of velocity wave motion in a struck string rigidly terminated at both its ends (and without losses) is shown in the figure below.

  Figure 4: Digital waveguide velocity-wave simulation of ideal lossless wave propagation on a string fixed at both ends (with strike initialization).

  

• For the struck string, simulation of velocity waves is more natural. Alternately, the initial velocity distribution could be integrated with respect to $x$ from $x = 0$, divided by $c$, and negated in the upper rail to obtain the equivalent initial displacement (since $v^{\pm} = \pm f^{\pm}/R = \mp c y^{\prime \pm}$, where $R$ is the wave impedance of the string).

• The simulation of displacement wave motion in a struck string rigidly terminated at both its ends (and without losses) is shown in the figure below (for the strike initialization shown above).

  Figure 5: Digital waveguide displacement-wave simulation of ideal lossless wave propagation on a string fixed at both ends (with strike initialization).