Mass Transmittance from String to String

Referring to Fig.9.15, the velocity transmittance from string 1 to string 2 may be defined as

By physical symmetry, we expect the transmittance to be the same in the opposite direction: . Assuming the incoming wave on string 2 is zero, we have , which we found in Eq.(9.16):

Thus, the mass transmittance for velocity waves is

We see that corresponds to , as befits a rigid termination. As , the transmittance becomes 1 and the mass has no effect, as desired.

We can now refine the picture of our scattering junction Fig.9.17 to obtain the form shown in Fig.9.18.

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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.