Make Music
Why does a short, tight string play a high note? And why does a bottle with more water sound higher when you blow, but lower when you tap? Find out and hear it.
- Frequency
- 328 Hz
- Nearest note
- E4 (-9¢)
- Mass per metre
- 0.39 g/m
- Wavelength on string
- 1.30 m
The maths, live
Mass per metre μ = ρ × π r²μ = 7850 × π × (0.125 mm)² = 0.39 g/mString f = (1 ÷ 2L) × √(T ÷ μ)f = (1 ÷ 1.30) × √(70 ÷ 0.00039) = 328 HzAdd water, then blow and tap. Blowing goes higher (less air to squash) but tapping goes lower (more weight to shake)!
How it works
A plucked string wobbles with its ends held still, so the longest wave that fits is twice the string's length. The frequency is f = (1 ÷ 2L) × √(T ÷ μ): a shorter string, a tighter string (more tension T) or a thinner, lighter string (less mass per metre μ) all give a higher note.
When you blow across a bottle, the air in the neck bounces up and down on the springy air inside, like a mass on a spring. Adding water leaves less air to squash, so the spring gets stiffer and the note goes up. Tapping is different: now the glass itself rings, and the water makes it heavier to shake, so the note goes down.
Try this
- Halve the string's length. What happens to the frequency? Which note do you get?
- Can you tune the string to A4 (440 Hz) using only the tension?
- Fill the bottle bit by bit and play a scale by blowing. Now tap it. Which way does the pitch go?