We stumbled into a home science demo today

Standing waves, and preferentially amplified random noise

Take a look at the below video (sound is a necessity in this case). Note that what she is holding there is a microphone with a speaker right below it, sort of “built into” the microphone. This is the exact product if anyone is curious. (So just to be clear - ball at the top is a microphone, cylinder right below it is a speaker.)

So what is going on here (near as I can tell)? The first, and easier thing, is just microphone feedback / amplification. There has to be some starting little sound that the microphone picks up, which the speaker then plays, which the microphone then picks up louder, which the speaker then plays louder, and so on, and you quickly build to a loud sound. In fact, if you put the microphone into the cup very carefully (without bumping the edges) it may be that nothing happens, but then if you tap the side of the cup and so give a little starting input, the sound will quickly build.

But why those particular pitches / frequencies of sound? That’s a little harder, but these are basically standing wave resonances. Standing waves (and click that to learn more) are stationary wave patterns that “fit” perfectly in a given geometry, and it is via standing wave resonances that any musical instrument “decides” what sound it will produce when you pluck that string or blow over that tube. You pluck the string, certain vibration wavelengths / patterns fit perfectly on the string (depending especially on how long the string is), most others do not, and that is how the guitar “knows” what sound to play.

Furthermore, lower frequencies / pitches correspond to longer wavelengths, which is why you are used to the fact that larger geometries / larger musical instruments produce lower sounds. In the video above, it is the air column that is vibrating (probably at first the length of air column between the speaker and end of the cup, approximately¹), and so as that length is shortened (by pushing the microphone further into the cup), we would expect the frequency goes up (higher pitch). Except I think, see below, that once speaker gets fully into the cup the vibration “shifts” so that air vibrating between the cup edges and speaker becomes the main vibration, a much smaller space, so you get that sudden shift to a much higher frequency.

BECAUSE… one more video below - when the geometry becomes more complicated, the sound becomes more interesting. Notice on this one you get the high pitch first, which almost certainly indicates it is the “horizontal” air column that is vibrating, between the speaker and the thin neck of the vase. (And for the lower pitches, if you put your hand need the top of the vase, you can feel the air rushing around, it’s quite impressive actually.)

1. It’s also possible some more complicated vibration pattern / geometry is what matters, but whatever it is that geometry is relatively large, compared to later.