AS Level Physics · Superposition. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
The principle of superposition: when two or more waves meet at a point, the resultant displacement is the sum of the displacements of the separate waves, with signs included.
A stationary wave forms when two progressive waves of the same frequency and similar amplitude travel in opposite directions and overlap, usually a wave and its reflection. At nodes the two waves always cancel, so the amplitude is zero. At antinodes they add to give the maximum amplitude. No energy is carried along a stationary wave.
The pattern is seen on a stretched string, in an air column, and with microwaves reflected from a metal plate. Measuring the spacing of the nodes gives the wavelength.
Students take the distance between two nodes as one whole wavelength. Adjacent nodes are only half a wavelength apart, so double the spacing to get λ.
Answer: 850 Hz
Try each one, then open the answer.
Answer: A. Adjacent nodes are λ/2 apart and an antinode lies halfway between them, so the node–antinode distance is λ/4.
Answer: B. By the principle of superposition the displacements add as vectors: +3.0 + (−1.0) = +2.0 cm.
Answer: C. Adjacent nodes are half a wavelength apart, so λ = 2 × 0.30 = 0.60 m.
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