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.
- Wave equationv = fλ
- Travelling wavey = A sin(kx − ωt)
On the syllabus
- GCSE Physics AQA 4.6.1wave speed, frequency and wavelength
- A-Level Physics AQA 3.3.1superposition and stationary waves
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.
Learn this properly
Lessons from GCSE Combined and Separate Science on this topic: worked steps, then exam-style questions with new numbers every time.
- Transverse and longitudinal wavesWaves and the electromagnetic spectrumFree
- Wave speed and measuring wavesWaves and the electromagnetic spectrumFree
See the whole courseThe full course, topic tests and mock papers come with Plus. See Plus
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.