# Reflection and Transmission of acoustic waves at a boundary

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1. Feb 22, 2017

1. The problem statement, all variables and given/known data
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 travelling 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.

2. Relevant 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:
$$\frac {A_t} {A_i} = \frac {2Z_1} {Z_1+Z_2} \text{ (3)}$$
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

2. Feb 22, 2017

### kuruman

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

3. Feb 22, 2017

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

4. Feb 22, 2017

### 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.

5. Feb 22, 2017