Resonance in the Home

A few weeks ago I heard this strange vibration sound in the house. It sounded like a motor and it wasn't immediately clear what it was. Eventually I figured out that it was coming from the toilet tank (see picture above). It turns out that the fill valve did not shut off completely, and water was continuously flowing through the valve and into the tank. This flowing movement caused vibrations in the fill valve which just happened to be at the same frequency as the natural frequency of the toilet tank. This is known as resonant frequency, and is something that designers of machinery (and perhaps toilet tanks too) try to avoid. It's an old tank so I don't know if such a thing would occur in a newer model of toilet tank. You can see in the picture how the vibrating tank caused waves to appear in the water. These waves are doing all sorts of interesting things, like reflect off boundaries and interfering with each other in some areas. If you measure the speed of the waves at the water surface, and the distance between them, you can calculate the vibration frequency.

Every substance has a natural frequency of vibration, known as its resonant frequency. It's the frequency that something will vibrate at if impacted by something, like a hammer. If you vibrate something at its resonant frequency it will experience "runaway" vibration in that the vibration energy will build up until the vibrations are very loud with high amplitude. In some cases this can even be destructive. Imagine pushing a swinging pendulum at a certain frequency. If you push it at just the right frequency the amplitude of the pendulum swing becomes greater and greater. It's the same idea as what happened with the toilet tank.