Pressure standing wave pattern, change cross sectional area

[snickersnee]

Homework Statement

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

Homework Equations

Antinodes (minimum pressure) at

Nodes (maximum pressure) at

[/B]

Equation for a standing wave:

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.

 

[CWatters]

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.

 

[snickersnee]

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.

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

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.