I have a closed how recipient with a cylinder form, something like this:

enter image description here

I have noticed that when I am dropping water through the hole, the collision of the water and the bottom of the recipient produces a sound. This sound changes depending on how full the recipient is, it has a low frequency when is very empty and a high frequency when is almost full. Is there a way to model this behavior? Could I know the level of the water inside the recipient by just hearing the sound produced?

I feel that it is needed to know the shape of the receivor (Volume, Diameter, Longitude), but let's suppose I have that information, and let's suppose that I am dropping pure water, I also feel that the trick is that the recipient must be closed to produce some kind of echo inside it, let's supposed it is closed

... How do I model the system?

  • 1
    $\begingroup$ It is 3D acoustic waves, so we could use 3D FEM and wave equation $u_{tt}-c^2\nabla^2u=0$ with $c=c_1$ in the water and $c=c_2$ in the air. Container also produces sound. We could consider the top as an elastic membrane, and for the rest we can use this code mathematica.stackexchange.com/questions/214279/… $\endgroup$ Apr 8, 2020 at 14:15
  • $\begingroup$ Have you tried modeling it as a Helmholtz resonator? $\endgroup$
    – nicoguaro
    Apr 8, 2020 at 15:23
  • $\begingroup$ Well, I tought about the Helmholtz Resonator, but I was not sure if it was correct $\endgroup$
    – Nau
    Apr 8, 2020 at 15:27
  • $\begingroup$ The most accurate way to do this would be experimentally: Use a microphone & ruler. Measure and plot water level vs. frequency, and voila, you have a model. You could try using different drip heights, bucket materials and dimensions, with / without a lid, etc... Another excuse not to fix the leaks in my roof. $\endgroup$ Apr 8, 2020 at 17:58

1 Answer 1


you model it as a helmholtz resonator, in which the mass element is the volume of air entrained within the entry spout on the top of the lid and the compliance element is the volume of air inside the container. That mass, when coupled with that compliance, results in a natural frequency of resonance. As the container progressively fills with water, the compliance becomes smaller and so the resonant frequency becomes higher.


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