Vocal chords vibrate to make their sounds. Smaller things just vibrate faster because they are smaller… with less size and weight, the cycle of going back and forth (which is what vibration is) just finishes faster and goes through the chords faster. Ergo, higher frequency, higher pitch.
This affects all kinds of things. Head into your kitchen and grab some glasses – what you drink water from made of actual glass or similar. Get 2 different glasses of different sizes. Set them down, leave them empty, and flick each one. The smaller one produces a higher pitched noise.
Latest Answers