Simplified Impedance Analysis
The above results are quickly derived from the general reflection-coefficient for force waves (or voltage waves, pressure waves, etc.):
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:
Since, by the Ohm's-law relations,
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