# Two definitions of wave reflection coefficient

by namphcar22
Tags: coefficient, definitions, reflection, wave
 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 $$R = \frac{v_2 - v_1}{v_2 + v_1}$$ where $v_i$ are the wave speeds in the two media. Later on, he writes the reflection coefficient in terms of mechanical impedance: $$R = \frac{Z_1 - Z_2}{Z_1 + Z_2}$$ where $Z_i$ 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?