Pipes and resonant mode with a node in exact center

AI Thread Summary
A pipe that can never have a resonant mode with a node in the exact center is one that is closed on both ends. This is because sound waves cannot escape, causing them to reflect back and forth without creating a node at the center. In contrast, an open pipe allows sound waves to pass through, preventing the necessary conditions for resonance. The discussion highlights that resonance requires specific boundary conditions, which are not met in a closed pipe scenario. Therefore, the conclusion is that a closed pipe cannot support a resonant mode with a node at the center.
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Homework Statement


What kind of pipe can never have a resonant mode with a node in the exact center? (choices are closed on both ends, open/closed on one end only. open on both ends) why?


Homework Equations


none given


The Attempt at a Solution


I think its closed on both ends because there is no where for the sound to escape, it keeps going back and forth threw the tube, but I am not sure.
 
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I'd go with the one open on both ends. In order to achieve resonance you need a bouncing surface. In the open pipe, the perturbation will pass right through and there won't be any waves colliding and interfering, hence, no resonance.
 

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