Determination of a string's impulse and step responses by Laplace transformation; relationships to exciting mechanisms
Ernst Terhardt · The Journal of the Acoustical Society of America · 1989
The excitation of a musical string is intimately dependent on the string's dynamic behavior—i.e., of the string alone—at the point of excitation. With resonable approximation that behavior can essentially be regarded as that of a linear system. An elegant way to describe it is by Laplace transformation. On the basis of the familiar equivalence of string and homogeneous electrical transmission line, the string impedance at the excitation point is expressed in Laplace-transform notation. This serves as a basis for getting the frequency characteristics of the impedance (magnitude and phase), and, by inverse Laplace transformation, the impulse and step responses of force and velocity, respectively. These characteristics of the string alone prove to be very helpful in discussing the interaction between a string and any exciting device such as a bow or piano hammer.