A level Physics · Edexcel 9PH0 · Topic 5B

Superposition and stationary waves

Key points

Principle of superposition: where two waves meet, the resultant displacement is the sum of the individual displacements.
Constructive interference happens when waves arrive in phase (path difference $n\lambda$ ); destructive when in antiphase (path difference $(n + \frac{1}{2})\lambda$ ).
Stationary (standing) waves form when two waves of the same frequency and amplitude travel in opposite directions, e.g. a wave reflected back along a string.
Nodes have zero amplitude; antinodes have maximum amplitude. Adjacent nodes are $\frac{\lambda}{2}$ apart. A stationary wave stores energy rather than transferring it.
For a string fixed at both ends, the fundamental has one antinode and $\lambda = 2l$ ; the frequency is $f = \frac{1}{2l}\sqrt{\frac{T}{\mu}}$ .
Core practical: vary the length, tension or mass per unit length of a string driven by a vibration generator and find the resonant frequencies.
Also measure the speed of sound in air by finding positions of maximum and minimum sound intensity in a stationary wave.

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When two waves meet, their displacements simply add. This principle explains interference and the stationary waves that form on strings and in air columns, which are the basis of musical instruments and of core practical 7.

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