Two definitions of wave reflection coefficient

by namphcar22
Tags: coefficient, definitions, reflection, wave
namphcar22 is offline
Jul31-11, 07:32 AM
P: 7
The waves book by A.P.French gives two characterizations of the reflection coefficient for a 1-D travelling wave encountering an interface between two media. On one hand, he writes
[tex] R = \frac{v_2 - v_1}{v_2 + v_1} [/tex]
where [itex]v_i[/itex] are the wave speeds in the two media. Later on, he writes the reflection coefficient in terms of mechanical impedance:
[tex] R = \frac{Z_1 - Z_2}{Z_1 + Z_2}[/tex]
where [itex]Z_i[/itex] denote the mechanical impedances for the media. My question is: are these two definitions always consistent? I two media have the same wave speed, do they automatically have the same impedance?
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