ACJC Superposition Lecture Notes

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 1 of 55 Superposition Guiding Questions Learning Objectives 1. What happens when waves meet an obstacle? (e) show an understanding of the terms diffraction, interference, coherence, phase difference and path difference 2. What happens when two or more waves meet? (a) explain and use the principle of superposition in simple applications. Two source interference (f) show an understanding of phenomena which demonstrate two- source interference using water waves, sound waves, light 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 = to solve problems for double-slit interference, where a is the slit separation and x is the fringe separation Single slit and multiple slits diffraction (i) recall and use the equation sinan = 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 = 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 b   for the resolving power of a single aperture, where b width of the aperture.

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 2 of 55 3. What is a stationary wave and how is it produced? (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 (b) show an understanding of experiments which demonstrate standing (stationary) waves using microwaves, stretched strings and air columns (d) determine the wavelength of sound using standing (stationary) waves Nature of Science Thomas Young and the Nature of Light From This Month in Physics History, The American Physical Society (May 2008) https://www.aps.org/publications/apsnews/200805/physicshistory.cfm The debate over whether light is a wave or a particle goes back many centuries. In the 17th century, Isaac Newton believed light was composed of a stream of corpuscles (little particles). At that time, a few scientists, most notably Dutch physicist and astronomer Christiaan Huygens, thought light was a wave vibrating in some sort of ether. Watch the video and discover their discoveries. https://youtu.be/1TL8eR geSnI?si=RBfK- p2grdeHqNIm

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 3 of 55 1. Diffraction The extent of spreading depends on the relative sizes of the opening and the wavelength of wave. Diffraction is most noticeable if the size of the opening is approximately equal to the wavelength of the wave. 1.1 Diffraction of Water Waves Diffraction can be demonstrated in the lab using water waves in a ripple tank experiment. Fig. 1.1 shows a water wave approaching a small opening. The parallel lines (which could be shadows in the ripple tank experiment) show the wavefronts – lines joining crests of the water wave If the wavelength is approximately the same size as the width of the opening, then the wave will diffract significantly as shown. Fig. 1.2 shows the same water wave approaching a bigger opening. If the wavelength of the wave is much smaller than the width of the opening, only the wave that emerge around the edge experienced some low level of diffraction while the centre portion remains largely unchanged. Fig. 1.1 – Schematic diagram showing water waves through a narrow gap Fig. 1.2 – Schematic diagram showing water waves through a wide gap Diffraction is the spreading of a wave into its geometrical shadow when it is incident on an edge of an obstacle or an aperture/opening. What happens when waves meet an obstacle?

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 4 of 55 While Fig . 1.1 & 1.2 shows the schematic diagram that you will usually draw to illustrate diffraction, Fig. 1.3 shows the actual water waves seen in a ripple tank experiment. Fig. 1.3 – Actual images showing water waves through a gaps of different sizes (source: T. Duncan – Advanced Physics) Explore the simulation on diffraction. Use the slider to vary the diameter of the hole and see its effects.

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 5 of 55 1.2 Diffraction of Longitudinal Waves (Sound Waves) Sound waves can diffract, for example, through a door opening. The width of the door (roughly a metre) is comparable to the wavelength of sound, and therefore, the sound waves diffract appreciably. This explains how we can hear someone approach the door although the person is not visually in sight. 1.3 Diffraction of Transverse Waves (Electromagnetic Waves) When visible light passes through a narrow slit (with slit width comparable to wavelength of light), it spreads beyond the narrow path defined by the slit into r egions that would be in geometrical shadow. This is shown in Fig 1.4. This phenomenon will be explained further in the subsequent sections. Explore this video on diffraction of sound. You can defer the interference segment until later of this topic. Fig. 1.4 (source: Young - College Physics)

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 6 of 55 2.1 Principle of Superposition 2.1.1 Superposition of Two Pulses with the Same Shape and Amplitude Fig. 2.1 shows the interaction between 2 crests as they approached each other while Fig. 2.2 shows the interaction between a crest and a trough. (a) Two crests, A and B, approaching each other. Both A and B have the same amplitude. (b) As the crests overlap, the net displacement at a point can be obtained by the vector sum of the individual displacement of each of the two crests. (c) The resultant displacement is the largest at this point in time. (d) As the crests move pass each other, they are not altered in anyway, as if the two crests were traveling along without ever interacting with the other wave. Fig. 2.2 shows the interaction if A is a crest while B is a trough. Fig. 2.2 Fig. 2.1 The principle of superposition states that the net displacement at a given place and time caused by two or more waves which traverse the same space and meet is the vector sum of the displacement which would have been produced by the individual waves separately at that position and instant of time. What happens when two or more waves meet?

Anglo-Chinese Junior College Lecture Notes Superposition H2 (9478) JC2 Physics 2026 Page 7 of 55 2.1.2 Superposition of Two Pulses with Different Shapes Fig. 2.3 and 2.4 show the superposition of pulses with different shape. The principle of superposition still applies here, where at every position along the rope, the resultant displacement is the vector sum of each of the individual displacements. Fig. 2.3 Fig. 2.4 Explore the simulation on wave interference. Use the slider to vary the amplitude of both the pulses and observe the effects. Explore the