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.