- #1

Blueman52

- 1

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## Homework Statement

Suppose a thin rod of silver (E = 83 GPa,

*[itex]\rho[/itex]*= 10.5 g/cm

^{3}) is joined to a thin rod of gold (E = 78 GPa,

*[itex]\rho[/itex]*= 19.3 g/cm

^{3}).

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 = [itex]\sqrt{\frac{E}{\rho}}[/itex] (velocity)

Z = [itex]\frac{AE}{v}[/itex] (impedance)

## The Attempt at a Solution

E

_{silver}= 83 x 10

^{9}Pa.

[itex]\rho[/itex]

_{silver}= 1.05 x 10

^{4}Kgm

^{-3}.

E

_{gold}= 78 x 10

^{9}Pa.

[itex]\rho[/itex]

_{gold}= 1.93 x 10

^{4}Kgm

^{-3}.

= 2.812 x 10

^{3}ms

^{-1}.

= 2.010 x 10

^{3}ms

^{-1}.

= 2.952 x 10

^{7}

= 3.881 x 10

^{7}

Z

_{silver}: Z

_{gold}

= 2.952 x 10

^{7}: 3.881 x 10

^{7}

= 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!