Standing waves on a string
PhysicsOscillations & WavesAges 16–17Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Oscillations & Waves
A string of length l has either both ends fixed or one end free. Change the vibrator frequency and wave speed to find the frequencies that produce standing waves; the simulation marks nodes, antinodes and wavelength, and checks the condition l = k·λ/2 (or l = (2k+1)·λ/4). The Lab screen adds tension T = mg from masses over a pulley and the mass per unit length μ, so v = √(T/μ): find resonance with a vibration generator or with a sonometer, tuning forks and a paper rider, or measure the AC mains frequency.
Lesson: Standing waves
What it shows
A standing wave forms when a wave travelling along a string reflects at the end and overlaps with itself. At certain frequencies the pattern stays in place: nodes never move and antinodes oscillate with maximum amplitude, λ/2 apart. With both ends fixed, l = k·λ/2; with one free end, l = (2k + 1)·λ/4. On the Lab screen the speed comes from the string itself, v = √(T/μ), with tension T = mg from a hanging mass and mass per unit length μ, so the first harmonic is f₁ = (1/2l)·√(T/μ).
How to use
Start from the defaults, use Snap f to nearest harmonic, then tick Right end free and compare. On Lab: tension and μ, choose Vibration generator (Melde), tune Generator frequency f for the largest amplitude and Record reading; repeat for other lengths, masses and strings and look at the graph. With Sonometer and forks, Strike the fork and change Vibrating length l until the paper rider is thrown off. Sonometer on AC mains finds the mains frequency.
Parameters you can change
- String length 0.4–3 m
- Wave speed 4–60 m/s
- Vibrator frequency 1–60 Hz
- Right end free
- Show oscillation envelope
- Screen Standing wave, Lab: tension and μ
- Experiment (Lab screen) Vibration generator (Melde's experiment), Sonometer and tuning forks, Sonometer on AC mains
- Hanging mass m (Lab screen) 0.05–5 kg
- String (Lab screen) String A (μ = 0.50 g/m), String B (μ = 1.00 g/m), String C (μ = 2.00 g/m), String X (μ unknown)
- Vibrating length l (Lab screen) 0.1–1.6 m
- Signal generator frequency (Lab screen) 1–200 Hz
- Tuning fork (Lab screen) 256 Hz, 288 Hz, 320 Hz, 384 Hz, 480 Hz, 512 Hz, Fork X (f unknown)
Questions to explore
- What fraction of a wavelength separates a node from the neighbouring antinode?
- For a string fixed at both ends, how do you calculate the lowest frequency that gives a standing wave?
- Why is a free end of the string always an antinode?
