Waves on a string
Frequency times wavelength gives the wave speed; add a second wave to see superposition and standing waves.
Readouts
What's happening
A travelling wave moves at v = fλ. When two identical waves travel in opposite directions they superpose: their displacements simply add. The result is a standing wave: points called nodes never move, while antinodes swing with double the amplitude. The string itself is the graph here: displacement versus position, animated in time.
GCSE Physics (AQA 4.6.1): wave speed, frequency and wavelength. A-Level Physics (AQA 3.3.1): superposition and stationary waves.
Work through the numbers with Physics Formulas.
Challenge
Predict first: with two waves on, how many nodes fit on the string if the wavelength is halved? Count them before and after.
Halving the wavelength doubles the number of nodes, because nodes sit every half-wavelength along the string.
FAQ
- How do you calculate wave speed?
- Wave speed equals frequency times wavelength, v = fλ. A 2 Hz wave with a 1.5 m wavelength travels at 3 m/s.
- What is a standing wave?
- Two identical waves travelling in opposite directions add up into a pattern that does not travel. Nodes never move and antinodes oscillate with twice the amplitude.
- How far apart are the nodes?
- Half a wavelength. So halving the wavelength doubles the number of nodes along the string.
- How do I find the wavelength from the speed and frequency?
- Rearrange v = fλ to λ = v/f. Sound at 340 m/s with a frequency of 512 Hz has λ = 340 / 512 = 0.664 m, and in a standing wave its nodes would sit 0.332 m apart. Pick Wavelength or Node spacing under Solve for to see each step.