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Two definitions of wave reflection coefficient 
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Jul3111, 07:32 AM

P: 7

The waves book by A.P.French gives two characterizations of the reflection coefficient for a 1D 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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