Normal modes in an oscillating system are special solutions where all the parts of the system are oscillating with the same frequency (called normal frequencies or allowed frequencies). The concept of normal modes is of vital importance in wave theory, optics and quantum mechanics.

On a string fixed at two points (like a guitar string, for instance) – the normal modes are shaped like sine waves. That’s why when you pluck a guitar string while sitting under flourescent lights – you can see a kind of bulging of the string at certain points – but relatively no motion at other points.

What does all this have to do with a circular drumhead? Well… Circular drumheads don’t have such nice sinusoidal modes. They are governed by much crazier math. The only reason I’m talking about them here is because I just had to make some animations of the different vibrational modes for one of my homework assignments, and because the animated gifs are really big… I’m going to make you click the “more” button to see them and think (“why did I care?”)

Now, obviously a drumhead doesn’t have as much amplitude when it oscillates… but if you ever wondered what kind of vibrational pattern is going on when you strike a drumhead – it’s probably a sum of a handful of those kind of vibrational modes.

Now you may resume the rest of your daily activities and pretend you never read this post.