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Pressure standing wave pattern, change cross sectional area

  1. Oct 12, 2015 #1
    1. The problem statement, all variables and given/known data

    See pictures. There are 2 parts to the problem but I can probably figure out the second part once I get the first part.


    upload_2015-10-12_17-28-9.png

    upload_2015-10-12_17-47-4.png


    2. Relevant equations

    Antinodes (minimum pressure) at upload_2015-10-12_17-43-56.png
    Nodes (maximum pressure) at upload_2015-10-12_17-44-53.png


    Equation for a standing wave: upload_2015-10-12_17-46-30.png
    3. The attempt at a solution

    Other than what I've written above, and that it's sinusoidal, not sure what the problem is looking for here. Any hints would be highly appreciated. Thanks for looking.
     
  2. jcsd
  3. Oct 15, 2015 #2

    CWatters

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    I think they are asking you to show where nodes and antinodes form. For example you normally get an antinode at the open end of a tube. However I'm not sure what you get at the transition between the two tubes. I never studied that.
     
  4. Oct 15, 2015 #3

    Hi thanks for responding. Here are the formulas for the reflection and transmission coefficients:

    upload_2015-10-15_14-40-36.png
    upload_2015-10-15_14-40-53.png
    where S1, S2 are cross sectional areas.

    R=1 if S2<<S1, a sudden strong area contraction almost acts as a rigid wall.

    R=-1 if S2>>S1, in this case the junction acts almost as a pressure-release surface.
     
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