- #1
Nerrad
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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