Travelling Waves on a String: Speed, Frequency, and Wavelength
1 · Predict
A string under fixed tension carries a travelling wave. If you drive it at a higher frequency, what happens to the wavelength?
- Wavelength gets shorter — wave speed stays fixed, so higher frequency squeezes the pattern.
- Wavelength gets longer at higher frequency.
- Wavelength doesn't change with frequency.
2 · Set Up
- Open the travelling-wave preset and press Reset. The string's tension (120 N) and linear density (0.01 kg/m) are fixed.
- Enable the wavelength readout on the string.
- Set the drive frequency for each trial and record the wavelength once the pattern is steady.
3 · Collect Data
| Drive frequency f (Hz) | Wave speed v (m/s) | Wavelength λ (m) |
|---|---|---|
| 220 | ||
| 440 | ||
| 880 |
Plot wavelength λ (y-axis) against 1/f (x-axis) for your three trials. Is the line straight through the origin?
4 · Analyze
- For one trial, compute v = √(T/μ) using T = 120 N and μ = 0.01 kg/m, then λ = v/f. Compare both to the table.
- Wave speed is the same in all three trials. Explain, using v = fλ, why doubling the frequency must halve the wavelength.
5 · Extend
- If you increased the string's tension instead of its frequency, would the wave speed increase or decrease? Would the wavelength at a fixed frequency get longer or shorter?
- A wave's speed depends on the medium (tension and linear density here), not on how fast you shake the string. Explain why frequency and wave speed are independent quantities that you set separately.
The Physics Behind This Experiment
Wave Speed on a String
The speed a transverse wave travels along a stretched string depends only on the string's tension and mass per unit length — not on frequency or amplitude.
Universal Wave Relation
For any wave, speed equals frequency times wavelength. Since v is fixed by the string, raising f forces λ to shrink proportionally.