Superposition & stationary waves
When two waves meet they don't collide — they pass right through one another, and where they overlap their displacements simply add. That single idea, the principle of superposition, is the key to this whole lesson. From it we build constructive and destructive interference (set by path and phase difference), then the beautiful standing patterns called stationary waves formed when two identical waves travel in opposite directions. We meet nodes and antinodes, learn that adjacent nodes are half a wavelength apart, work through the harmonics of a stretched string and of open and closed air columns, compare stationary with progressive waves, and finish by using a stationary wave to measure a wavelength — and from it the speed of sound.
By the end you should be able to (NSSCAS Physics (AS) 2.6):
- State and use the principle of superposition: when waves meet, the resultant displacement is the sum of their individual displacements
- Explain constructive and destructive interference in terms of path difference (nλ and (n+½)λ) and phase difference
- Explain the formation of a stationary wave from two identical progressive waves travelling in opposite directions, using a graphical method
- Identify nodes (zero amplitude) and antinodes (maximum amplitude) and recall that the distance between adjacent nodes is λ/2
- Describe stationary waves on a stretched string and the harmonics it produces (fₙ = nv/2L)
- Describe stationary waves in air columns for pipes open at both ends and closed at one end, and the harmonics each produces
- Compare the properties of stationary and progressive waves
- Use stationary waves to measure a wavelength, and hence determine the speed of a wave such as sound
Miss Elizabeth and Mike talk through the whole topic — with the figure and working drawn live.