Waves on a string sim
Tune a vibration generator until standing waves appear, measure the nodes, and find the wave speed from v = f λ and a graph of f against 1/λ.
General wave properties · covers the O-Level, IGCSE, GCSE topic
What the sim shows
The vibration generator shakes one end of the string at the frequency f set on the signal generator. Waves travel to the bridge, reflect, and the waves going each way add together. Only at certain frequencies does a whole number of loops fit between the vibrator and the bridge: this is a standing wave. At the nodes the string does not move; at the antinodes it moves the most. One loop is half a wavelength, so λ = 2L ÷ n (L = vibrating length, n = number of loops), and the wave speed is v = f λ. With 100 g hanging (tension T = m g = 0.100 × 9.81 = 0.98 N) and L = 1.200 m, 1, 2 and 3 loops appear at about 13.1, 26.1 and 39.2 Hz, and each time v = f λ ≈ 31.3 m/s. Double the frequency and the wavelength halves, so the speed stays the same: it depends on the string and how tightly it is stretched, not on the frequency. That is why the graph of f against 1/λ is a straight line through the origin with gradient v. Four times the mass (400 g) gives twice the speed, 62.6 m/s. (For this string v = √(T/μ) with μ = 1.0 g/m; you do not need this formula.) Real results scatter: the loops are only clear within about f/30 of each resonance, a node is hard to judge to better than about 2 mm, and the rule reads to 1 mm, so your v may differ from 31.3 m/s by about 1 %. Limits of the model: the vibrator end is treated as almost a perfect node (a real one moves slightly), the string does not stretch, the cord beyond the bridge is not shown vibrating, every resonance is drawn with the same loop size (50 mm), and the motion is shown as the blur your eye sees, or slowed to 1 Hz by the strobe, not at its real speed. The strip under the bench is the same string close up, at true scale. Nothing happens unless you act: each drag or button press is one step.
- Drive pin: the vibrator shakes this end of the string
- String: a blur where it moves, still at the nodes
- Markers A and B: line them up with nodes in the close-up strip; they read to 1 mm
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