Longitudinal wave from one thin rod to another

[Blueman52]

Homework Statement

Suppose a thin rod of silver (E = 83 GPa, $\rho$ = 10.5 g/cm³) is joined to a thin rod of gold (E = 78 GPa, $\rho$ = 19.3 g/cm³).
Both rods have the same cross sectional area, and a longitudinal wave passes from the silver into the gold.

What amplitude will the transmitted and reflected waves be if the incident wave has amplitude 1?

Homework Equations

v = $\sqrt{\frac{E}{\rho}}$ (velocity)
Z = $\frac{AE}{v}$ (impedance)

The Attempt at a Solution

E_silver = 83 x 10⁹ Pa.
$\rho$_silver = 1.05 x 10⁴ Kgm^-3.

E_gold = 78 x 10⁹ Pa.
$\rho$_gold = 1.93 x 10⁴ Kgm^-3.

= 2.812 x 10³ ms^-1.

= 2.010 x 10³ ms^-1.

= 2.952 x 10⁷

= 3.881 x 10⁷

Z_silver : Z_gold
= 2.952 x 10⁷ : 3.881 x 10⁷
= 0.761 : 1


This is as far as I got.
I presume I have to multiply the amplitude with Z_silver : Z_gold
= 1 x 0.761
= 0.761

but I don't know whether this is the amplitude of the reflected or transferred wave.

I would greatly appreciate any help at all.
Thank you!

 

[ideasrule]

I would approach the problem by setting up a coordinate system with x=0 as the boundary. To the left, the wave is Ae^ik1*x + B^-ik1*x at t=0, where A is the initial wave and B is the reflection. To the right, it's Ce^ik2*x. You can calculate B/A and C/A by applying the appropriate boundary conditions.