For a science project I chose to investigate the relationship between the resonance frequency of cups and the amount of water filled in it. I filled the cup with 10 grams of water each time, and used a pencil to hit the cup. After trying a lot of combinations, I found that there is a linear relationship between $1/f^2$ and $m^3$, where $f$ is the resonance frequency and $m$ is the mass of water added. Can anyone explain this relationship? I searched all over the internet, but I couldn't find anything.
I used cups that are cylindrical, so the mass can be converted into water level and the relationship maybe between $1/f^2$ and $h^3$ where $h$ is the water level.
These are my research that I think are most relevant:
Maybe the cups can be modeled as a spring-mass model? The guy in the first link said, "resonant frequency always looks like the square root of some kind of restoring force divided by some kind of inertia"
Something like this: