What it shows
An air column closed at one end resonates when its length is a quarter or three quarters of the wavelength. Two resonance lengths give the speed of sound without needing to know the end correction.
The science
A column of air closed at the bottom by water resonates when a standing wave fits, with a node at the water and an antinode just above the open end. The first resonance occurs at a length L1 + e = λ / 4 and the second at L2 + e = 3λ / 4, where e is the end correction of about 0.6 times the tube radius. Subtracting gives L2 − L1 = λ / 2, so the speed is v = f λ = 2 f (L2 − L1). At 30 degrees C the speed of sound in air is about 349 m/s, rising 0.6 m/s for each degree.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A tall glass or plastic tube about 60 cm long and 3 to 4 cm wide (a clear PVC pipe or a long measuring cylinder)
- A large bucket or tall jar of water that the tube can dip into
- A phone with a tone generator app set to 512 Hz or a tuning fork
- A metre rule and a clamp or stand
- A pencil and a notebook
Safety
For this project: Keep the volume modest to protect hearing. An adult should help if glass is 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
8 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.
Clamp the tube vertically with its lower end dipped in the water, the tube and bucket making a closed air column of adjustable length.
Hold the phone speaker just above the open end and play the 512 Hz tone at a steady volume.
Slowly raise the tube out of the water, listening for the length at which the sound suddenly gets louder; mark the length of the air column L1.
Raise the tube further and find the second louder position L2, about three times the first.
Repeat three times and average each length, noting whether the readings go up or down with the tube.
Calculate λ = 2 (L2 − L1) and v = f λ.
Calculate the end correction e = (L2 − 3 L1) / 2 and compare with 0.6 r.
Repeat with a 440 Hz tone to see that v stays the same although the lengths change.
What you should see
The speed of sound is found to be about 330 to 350 m/s, close to the expected value for the room temperature, and the end correction is about 1 to 2 cm.
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 resonance?
A large vibration that builds up when the driving frequency matches a natural frequency of the system.
2Why use two resonance lengths?
Their difference equals half a wavelength, which removes the unknown end correction.
3What is the first resonance length in terms of λ?
L1 + e = λ / 4.
4How does temperature change the speed of sound?
It rises by about 0.6 m/s for each degree Celsius rise.
Take it further
Repeat on a cold morning and a hot afternoon to see the speed of sound changing with temperature.
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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