# How full a recipient is by hearing its sound frequency

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

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?

• 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/… Apr 8 '20 at 14:15
• Have you tried modeling it as a Helmholtz resonator? Apr 8 '20 at 15:23
• Well, I tought about the Helmholtz Resonator, but I was not sure if it was correct Apr 8 '20 at 15:27
• 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.
– sven
Apr 8 '20 at 17:58