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Reflection and Transmission of acoustic waves at a boundary

  1. Feb 22, 2017 #1
    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. jcsd
  3. Feb 22, 2017 #2

    kuruman

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    Read this carefully. You are asked to find the reflected and transmitted amplitudes relative to the incident wave amplitude. What does that mean?
     
  4. Feb 22, 2017 #3
    Does it have something to do with ratio? To me it's quite vague
     
  5. Feb 22, 2017 #4

    kuruman

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    Yes, it has to do with ratio. Call the incident amplitude 1 and find the reflected and transmitted amplitudes as a fraction of 1.
     
  6. Feb 22, 2017 #5
    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?
     
  7. Feb 22, 2017 #6

    kuruman

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    Exactly.
     
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