Reflection and Transmission of acoustic waves at a boundary

[Nerrad]

Homework Statement

An interface is formed between a block of aluminium (density = $2.70 \times 10^3 kg/m^3$, speed of sound =$6.40 \times 10^3m/s$) and a block of copper (density = $8.96 \times 10^3 kg/m^3$, speed of sound =$4.76 \times 10^3m/s$). Longitudinal waves traveling through the aluminium are normally incident on the boundary, and are partially reflected. Calculate:
(a) The acoustic (characteristic) impedances of aluminium and copper;
(b) The amplitudes of the reflected and transmitted waves, relative to the incident wave;
(c) The percentage of the incident power that is transmitted and reflected.

Homework Equations

(a) The acoustic characteristic impedance of a material is given by:
$$Z = \rho v \text{ (1)}$$
where $\rho$ is equal to the density of the material and $v$ is the acoustic velocity
(b) Reflection coefficient is given by :
$$\frac {A_r} {A_i} = \frac {Z_1-Z_2} {Z_1+Z_2} \text{ (2)}$$
Transmission coefficient is given by:
$$\frac {A_t} {A_i} = \frac {2Z_1} {Z_1+Z_2} \text{ (3)}$$

The Attempt at a Solution

(a) By using equation 1, I've obtained impedances of $1.73 \times 10^7$ and $4.33 \times 10^7$ respectively.
(b) I have to work out the amplitudes relative to the incident wave, but I'm not given the amplitude of incident wave, so how do I go about tackling this question? Thanks

 

[kuruman]

b) The amplitudes of the reflected and transmitted waves, relative to the incident wave;

Read this carefully. You are asked to find the reflected and transmitted amplitudes relative to the incident wave amplitude. What does that mean?

 

[Nerrad]

Read this carefully. You are asked to find the reflected and transmitted amplitudes relative to the incident wave amplitude. What does that mean?

Does it have something to do with ratio? To me it's quite vague

 

[kuruman]

Yes, it has to do with ratio. Call the incident amplitude 1 and find the reflected and transmitted amplitudes as a fraction of 1.

 

[Nerrad]

Yes, it has to do with ratio. Call the incident amplitude 1 and find the reflected and transmitted amplitudes as a fraction of 1.

Oh so what you mean is that it doesn't matter what I set the incident amplitude as, because at the end I'm going to get a percentage/ratio of it? Kinda like how for probability it all adds up to 1?

 

[kuruman]

Exactly.