Standing waves in an open pipe
Physics and electronics discussion, revision, exam and homework help.
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Standing waves in an open pipeThink of standing sound waves in a pipe open at both ends. Since we seem to call the ends of the pipe 'nodes' or 'antinodes', the phase of the wave at the ends seems to differ by a multiple of pi/2. Does anyone know why there can't be other phase differences?
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Re: Standing waves in an open pipeThere is always an antinode at an open end and a node at a closed end.
The node at the closed end is there because the solid end stops any motion of the medium and naturally creates a point of zero displacement.
At the open end the wave passes into a region (the outside) where its velocity is greater than inside.
This is effectively a wave moving from a dense to a less dense medium similarly to light moving from glass to air. When a wave does this it undergoes a partial reflection at the boundary but with no phase change.
The lack of phase change means the reflected wave reinforces the incident wave creating an antinode.
Either the wave undergoes no phase change or it undergoes complete reversal (a 180 deg phase change.)Last edited by Stonebridge; 02-06-2012 at 08:15. -
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Re: Standing waves in an open pipeIs it that the pressure buildup by the wave has little place to go (pressure is harder to transmit through a 'less dense' medium,) so it collapses back on itself? By the logic, I wonder if sound waves going into a pipe get reflected with a phase reversal, because they lose all their pressure at the boundary quite easily.
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Re: Standing waves in an open pipeThe simplest explanation I can think of at the moment is that the boundary is a place of discontinuity. The wave suddenly speeds up or slows down. Mechanically this requires a change in a value of a force, which in turn will have a Newton 3 reaction in the opposite direction, causing a reflection.
The maths is actually beyond A Level but if you are interested you may find something if you search for it under "reflection of waves at a boundary" or similar.
Your idea about pressure is also good. There will need to be a pressure change at the boundary. Pressure is force/area meaning a force change.
