#### Simplified Impedance Analysis

The above results are quickly derived from the general reflection-coefficient for force waves (or voltage waves, pressure waves, etc.):  (10.17)

where is the reflection coefficient of impedance as seen'' from impedance . If a force wave traveling along in impedance suddenly hits a new impedance , the wave will split into a reflected wave , and a transmitted wave . It therefore follows that a velocity wave will split into a reflected wave and transmitted wave . This rule is derived in §C.8.4 (and implicitly above as well). In the mass-string-collision problem, we can immediately write down the force reflectance of the mass as seen from either string: That is, waves in the string are traveling through wave impedance , and when they hit the mass, they are hitting the series combination of the mass impedance and the wave impedance of the string on the other side of the mass. Thus, in terms of Eq. (9.17) above, and . Since, by the Ohm's-law relations, we have that the velocity reflectance is simply Next Section:
Mass Transmittance from String to String
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Mass Reflectance from Either String