What it shows
Air in a bottle with a narrow neck resonates at a frequency that falls as the bottle’s air volume gets bigger. Adding water makes the note rise.
The science
The air in the neck acts as a mass and the air in the body as a spring. The resonant frequency of such a Helmholtz resonator is f = (v / 2π) √(A / (V L)), where A is the neck’s area, L its effective length, V the air volume and v the speed of sound. So f is proportional to 1 / √V: a bigger air volume gives a lower note. The same principle sets the sound of a blown bottle, a guitar’s sound hole and a car exhaust.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A glass or plastic bottle with a neck about 2 cm wide
- A measuring jug and water
- A phone with a tuner or spectrum analyser app
- A ruler to measure the neck and the bottle
- A set of 4 to 5 similar bottles of different size (optional)
- Graph paper
Safety
For this project: An adult should supervise if glass bottles are used.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Measure the bottle’s total volume by filling it from the jug, then empty it.
Blow gently across the top edge of the empty bottle until it hums, and read the frequency from the phone app.
Add 100 mL of water, so the air volume falls by that amount, and read the new frequency.
Continue to add 100 mL at a time, noting V (the air volume left) and f each time, until the bottle is almost full.
Calculate 1 / √V for each row in a table.
Plot f against 1 / √V and see that the points lie on a straight line through the origin.
Measure the neck’s diameter and length, calculate A and L, and compare the predicted frequency for the empty bottle with the measured one.
What you should see
The pitch rises as water is added, and f plotted against 1 / √V is nearly a straight line. The predicted frequency for the empty bottle is close to the measured one.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is a Helmholtz resonator?
A cavity of air with a narrow neck in which the air in the neck vibrates against the springiness of the air inside.
2Why does the note rise when water is added?
The air volume V falls and f is proportional to 1 / √V.
3What changes if the neck is wider?
The area A is larger, so the frequency rises.
4Where else does this principle occur?
In guitar bodies, ocarinas and bass-reflex speakers.
Take it further
Blow across bottles with different neck lengths cut from plastic and show the effect of L on the frequency.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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