Waves & Sound
Travelling wave on a string
Press Play — watch y = A sin(kx − ωt) propagate; probe y(t) at the string centre.
Travelling wave on a string — interactive Waves & Sound simulation. Press Play — watch y = A sin(kx − ωt) propagate; probe y(t) at the string centre. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Travelling wave
A sinusoidal disturbance travels along a string with speed v = √(T/μ).
Each point oscillates transversely while the pattern moves along the string. The wave number k and angular frequency ω are linked by the dispersion relation for a string.
- y = A sin(kx − ωt)
- v = √(T/μ)
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A string under fixed tension carries a travelling wave. If you drive it at a higher frequency, what happens to the wavelength?
Predictions to weigh
- 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.
Variable roles
What you set:
- Drive frequency f (Hz)
What you measure:
- Wave speed v (m/s)
- Wavelength λ (m)
How the investigation runs
- 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.
Governing equation
Wave Speed on a String — v = √(T/μ)
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 — v = f·λ
For any wave, speed equals frequency times wavelength. Since v is fixed by the string, raising f forces λ to shrink proportionally.
What the printable worksheet asks students to work out
- 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.
Where this shows up beyond the lab
- 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.
- AP Physics 2 — Unit 14: Waves, Sound, and Physical Optics
- IB Physics — C.2 Wave model
- General High School Physics — Waves & sound
- NGSS High School Physics — Wave properties
- Middle School Physical Science — Wave amplitude and energy
- Middle School Physical Science — Waves meeting materials
- Welcome to Travelling Wave
- Select the string
- Press Play
- Watch it move
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.