EJC Physics H212a Superposition 2023 1. Notes (full)

9749(202 3) H2 Physics H212 Superposition – Notes Page 1 of 28 H2 Topic 12a – Superposition Anti-reflection (AR) coating commonly found on lenses, and Active Noise Cancellation (ANC) commonly found on higher -end audio devices are just two amongst many applications of interference, which is a phenomenon based on the principle of superposition. Content • Principle of superposition • Stationary waves • Diffraction • Two-source interference • Single slit and multiple slit diffraction Learning Outcomes Candidates should be able to: (a) explain and use the principle of superposition in simple applications (b) show an understanding of the terms interference, coherence, phase difference and path difference (c) show an understanding of experiments which demonstrate stationary waves using microwaves, stretched strings and air columns (d) explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes (e) explain the meaning of the term diffraction (f) show an understanding of experiments which demonstrate diffraction including the diffraction of water waves in a ripple tank with both a wide gap and a narrow gap (g) show an understanding of experiments which demonstrate two-source interference using water waves, sound waves, light and microwaves (h) show an understanding of the conditions required for two-source interference fringes to be observed (i) recall and solve problems using the equation λ = ax / D for double-slit interference using light (j) recall and use the equation sinθ = λ / b to locate the position of the first minima for single slit diffraction (k) recall and use the Rayleigh criterion θ ≈ λ / b for the resolving power of a single aperture (l) recall and use the equation d sinθ = nλ to locate the positions of the principal maxima produced by a diffraction grating (m) describe the use of a diffraction grating to determine the wavelength of light (the structure and use of a spectrometer are not required) incoming noise 2nd sound introduced silence

9749(202 3) H2 Physics H212 Superposition – Notes Page 2 of 28 12.0 Introduction Unlike particles, two (or more) waves can exist at the same point in space, at the same time. In this topic, we will look at the interaction between two or more waves when they meet and overlap. 12.1 Principle of Superposition Be careful to use “displacement” rather than “amplitude” when defining superposition. In a wave, the displacement of each particle or segment of the wave varies from zero to the maximum possible value, and therefore the resultant displacement when multiple waves meet will change with time Example 1 On the same axes, use the principle of superposition to sketch the resultant variation of displacement with time when two waves A and B meet and overlap at a single particle. Note: the principle of superposition applies at each point along the wave, at the same point in tim