RI Chap 11 Superposition Lecture Notes

11 SUPERPOSITION H2 Physics 9478 Content Page 11.1 Principle of Superposition 2 11.2 Standing Waves 3 11.3 Diffraction Through a Finite-size Gap 14 11.4 Interference of Two or More Coherent Sources 15 11.5 Single-Slit Diffraction 30 11.6 Appendix 39 Learning Outcomes Candidates should be able to: (a) explain and use the principle of superposition in simple applications (b) show an understanding of experiments which demonstrate standing (stationary) waves using microwaves, stretched strings and air columns. (c) explain the formation of a standing (stationary) wave using a graphical method, and identify nodes and antinodes, differentiating between pressure and displacement nodes and antinodes for sound waves. (d) determine the wavelength of sound using standing (stationary) waves. (e) show an understanding of the terms interference, coherence, phase difference and path difference. (f) show an understanding of phenomena which demonstrate two- source interference using water waves, sound waves, light waves and microwaves. (g) show an understanding of the conditions required for two- source interference fringes to be observed. (h) recall and use the equation ax D λ= to solve problems for double-slit interference, where a is the slit separation and x is the fringe separation. (i) recall and use the equation sinan θλ= to solve problems involving the principal maxima of a diffraction grating, where a is the slit separation. (j) describe the use of a diffraction grating to determine the wavelength of light (knowledge of the structure and use of a spectrometer is not required). (k) show an understanding of phenomena which demonstrate diffraction through a single slit or aperture, or across an edge, such as the diffraction of water waves in a ripple tank with both a wide gap and a narrow gap, or the diffraction of sound waves from loudspeakers or around corners. (l) recall and use the equation sinb θλ= to solve problems involving the positions of the first minima for diffraction through a single slit of width b. (m) recall and use the Rayleigh criterion bθλ≈ for the resolving power of a single aperture.

Page| 2 11.1 Principle of Superposition  Introduction A wave is a disturbance that travels through a medium or vacuum. For mechanical waves, like sound and water waves, the disturbance refers to the displacement of the particles of the media from their equilibrium position. For electromagnetic waves, the dist urbance refers to the varying electric and magnetic field. What happens when two waves of the same type (e.g., sound waves from two sources) meet at a point in space? Fig. 11.1 illustrates two different sets of two waves meeting at an instant of time. Fig. 11.1 Note that displacement of the resultant wave at any position is the vector sum of the displacements due to the two waves. -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0 1 2 3 4 5 6 7 8 9 10 Resultant Wave Wave