Quick answer: A stationary wave forms when two identical waves travel in opposite directions and superpose, giving fixed nodes and antinodes. This Physics 11-12 lab on stationary waves gives the aim, the equipment, the safety points, a step-by-step method, sample results and 8 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How can resonance in an air column measure the speed of sound? Use tuning forks of known frequency and a tube dipped in water, find the first loud position for each fork and use a graph of length against 1/f to find the speed and the end correction.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB C.4
Aim
To find the speed of sound in air and the end correction using resonance in a tube closed at one end.
Equipment
- Open glass tube about 60 cm long and 2 cm radius (inner diameter 4 cm)
- Tall measuring cylinder or pipe filled with water
- Set of tuning forks (256, 320, 384 and 512 Hz) and a rubber pad
- Metre rule, thermometer
Safety
Handle glass tubing carefully and stand the cylinder on a tray so spills are contained. Strike tuning forks on a rubber pad, never on the bench or on glass, and keep the forks away from your face.
Method
- Stand the tube in the water so the air column is short and hold a vibrating fork just above the open end.
- Raise the tube slowly until the sound becomes loudest. Measure the length L of the air column above the water to the nearest millimetre.
- Repeat three times and take the mean.
- Repeat for the other forks, recording the room temperature.
- Calculate 1/f for each fork and plot L against 1/f.
Results
Sample first-resonance lengths (mean of three), room temperature 20 °C:
| f / Hz | 1/f / 10⁻³ s | L / m |
|---|---|---|
| 256 | 3.906 | 0.326 |
| 320 | 3.125 | 0.259 |
| 384 | 2.604 | 0.214 |
| 512 | 1.953 | 0.158 |
Analysis questions
Question 1 Resonance condition
Explain why the first resonance occurs when L + e = λ/4, where e is the end correction.Question 2 Line equation
Use v = fλ to show that L = v/(4f) − e. State what to plot.Question 3 Slope of the line
Find the slope of the line of L against 1/f from the 256 Hz and 512 Hz readings.Question 4 Speed of sound
Calculate the speed of sound from the gradient.Question 5 End correction
Calculate the intercept and state the end correction.Question 6 Percentage difference
The accepted value of v at 20 °C is 343 m/s. Calculate the percentage difference.Question 7 Second resonance
For the 512 Hz fork the second resonance is found at L₂ = 0.493 m. Use L₁ and L₂ to find v without needing e.Question 8 Uncertainty and improvement
Estimate the percentage uncertainty in L for the 512 Hz fork if the loudest position is uncertain by ±3 mm, and suggest one improvement.
