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I understand that both open and closed-end air columns have many resonant frequencies, called harmonics and a fundamental frequency. At these frequencies, we expect to observe standing waves of maximum strength that are as close to full destructive and constructive interference correct? We also expect to observe a given amount of nodes and antinodes, and a specific number of waves in the column, given that waves of a certain frequency are propagating in the column.

My main question is what is the behavior when we are not at these harmonics? We still observe standing waves of course, but is our response less strong - meaning that destructive and constructive interference is not as "perfect?" Also how is the amount of nodes and other things like the number of waves predicted? Say at my ~180 Hz harmonic I predict 1 node and 2 antinodes, and at my ~360 Hz harmonics I predict 2 nodes and 3 antinodes. What would I predict at say 230 Hz, or 300 Hz?

Thank you!

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    $\begingroup$ We (almost) always observe a reflected wave but we only observe a standing wave when the reflected wave is coming back at the right phase so that it can cancel the incident wave at certain fixed points, the nodes. This is a resonance condition that, when the frequency is given, depends on the length between the generator and the discontinuity at which the reflection occurs. $\endgroup$
    – hyportnex
    Commented Nov 23, 2023 at 20:20

2 Answers 2

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We still observe standing waves $\dots$
The boundary conditions at the two ends would hold but for the frequencies that you asked about there would be no nodes or antinodes in between the two ends of the column.

The column is excited at the forcing frequency and the oscillations die away relatively quickly.

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We still observe standing waves of course

No, we don't.

At the end of the the tube, the wave gets reflected so we always have a forward and a backward travelling wave. If the two waves always meet at the same place, they interfere with each other the same way and we get nodes and antinodes are well defined locations. That's what "standing" wave means.

This only happens for certain wavelengths (the fundamental and the harmonics). If the wavelength is different, there is no standing pattern: the "meeting points" of the wave move around constantly, so we get a "travelling" wave. Since the forward and backward travelling wave constantly change phase, they interfere with each other more or less randomly and will cancel.

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  • $\begingroup$ So are standing waves only when the incident wave and reflected wave line up at certain spots to result in complete destructive interference and constructive interference? I ask because I had a set up with a speaker and a microphone, and intentionally drove it at frequencies that were not harmonics. In this setup, I still saw waves that looked like standing waves on the oscilloscope in the sense that they did not change in time, but the amplitudes changed based on position in the tube. This is just the constructive and destructive interference of waves, but not standing waves then? $\endgroup$
    – Sonite
    Commented Nov 23, 2023 at 21:10
  • $\begingroup$ With this set up, I normalized all my results. So the amplitude was a % of the maximum, and the distance is normalized by the wavelength. And I observed points of minima and maxima separated by half of a wavelength. With minima at the beginning and end. So to me it seemed like the only difference between this and a standing wave was strength of interference, because these maxima and minima occurred in a recurring pattern separated by half a wavelength. However the minima was never a perfect minima and the maxima was never a perfect maxima. $\endgroup$
    – Sonite
    Commented Nov 23, 2023 at 21:39

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