Force Wave Mass-String Model

The velocity transmittance is readily converted to a force transmittance using the Ohm's-law relations:

Calculating it for the other direction as a check gives

Thus, while the reflectance of the mass toggles sign when going from force to velocity waves, the transmittance of the mass is the same in all cases. We therefore have the force-wave scattering junction shown in Fig.9.19.

Checking as before, we see that corresponds to , which means no force is transmitted through an infinite mass, which is reasonable. As , the force transmittance becomes 1 and the mass has no effect, as desired.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.