ASRJC Superposition Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 10-1 Additional Notes Topic 12: Superposition Learning Outcomes: Candidates should be able to: A. Principle of superposition (a) explain and use the principle of super position in simple applications (b) show an understanding of the terms interference, coherence, phase difference and path difference B. Two-source interference (g) show an understanding of experiments which demonstrate two -source interference using water waves, sound waves, light waves 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 C. Single slit diffraction (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 (j) recall and use the equation sin 𝜃 = 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 D. Multiple slit diffraction – diffraction grating (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) E. Stationary waves (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 Suggested Lecture Plan Lect Concepts Qns Est. Video Time 1 A, B.1, B.2 CYU 1 40 min 2 B.3, B.4, C.1 Eg 1, Eg 2, Eg 3 42 min 3 C.2, C.3, C.4 Eg 4, Eg 5 42 min 4 C.5, D.1, D.2, E.1, E.2 Eg 6, Eg 7, Eg 8 36 min 5 E.3, E.4, E.5, E.6.1, E.6.2 CYU 2, Eg 9, Eg 10 38 min 6 E.6.3, E.6.4, E.6.5 Eg 11, Eg 12 46 min

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 10-2 Additional Notes Wave Nature of Wave Properties of Waves Behaviour of Wave Periodic Motion Disturbance through Space and Time Transfer Energy Not Matter Most Wave Types require Material Medium for Propagation, except EM Waves which can propagate in a vacuum as well as in a material medium. Transverse and Longitudinal Waves Wave speed Frequency Wavelength Amplitude Transverse Wave Crest & Trough Longitudinal Wave Rarefaction & Compression Superposition Single Slit Diffraction Stationary Waves Two-Source Interference Multiple Slit Diffraction

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 10-3 Additional Notes In this topic we are concerned with the interaction between two or more waves. What happens when two or more waves meet? • The waves must be of the same type (ie. light and sound wave cannot superpose but light and x-rays can) and if they are transverse waves, the direction of their polarisation must be the same. Guiding questions to help you navigate and understand the topic better: 1. What is the principle of superposition? 2. What are the general contexts under which it can be applied? A. Two-source interference – when waves from two sources overlap B. Single slit diffraction – when a wave passes through a single slit C. Multiple slit diffraction – when a wave passes through many slits D. Stationary waves – when two waves moving in opposite directions overlap 3. How is the principle of superposition being applied in these contexts? 4. What are the patterns that arise out of the interaction of waves in each of these contexts? Check Your Understanding 1 (solution and explanation in SLS). Select the scenario(s) where you think it makes sense to invoke the Principle of Superposition. You may select more than one option.  A sound wave travels from A to B and a light wave travels from B to A.  A sound wave from a tuning fork travels from A to B and a sound wave from another tuning fork of lower pitch travels from B to A.  A beam of red laser light travels from A to B and a beam of green laser light travels from B to A.  You are dancing as music plays from both sides of your headphones / earphones.  Your teacher asks the class a question. You raise your hand and offer a possible answer. The Principle of Superposition states that when two waves meet at a point, the resultant displacement is equal to the vector sum of the individual displacements. A Principle of Superposition Crest Meets Crest Crest Meets Trough Memorize Scan for animation of two pulses approaching each other in-phase / anti-phase

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 10-4 Additional Notes Key Term: Interference When two or more waves overlap and interact, we say they interfere with each other. Interference is an effect that occurs when two or more waves overlap to produce a new wave pattern, i.e. a change in amplitude. B.1 General patterns using water waves Some visualisations: Ripple Tank Experimental setup and observations • Two dippers, attached to the vibrator, are set into vertical vibrations with the same amplitude, frequency and phase (in phase). • By projecting the light from the lamp such that it passes through the water onto the white screen below, an interference pattern will be easily detected. • A snapshot of the interference pattern observed is as shown. Note the lines of constructive interference (alternating bright and dark regions) and destructive interference (dark lines). B Two-Source Interference Source for left and centre picture: Fabric of the Cosmos by Brian Greene Source for picture on the right: The Original Double Slit Experiment by Derek Muller

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 10-5 Additional Notes B.1.1 General patterns using water waves – Mapping path differences Fig. 1 below shows a time -freeze diagram of waves from two sources, S 1 and S2. The two sources are coherent, and are in phase (phase difference = 0). Key term: Coherence Coherent sources are sources which produce waves of the same frequency with a constant phase difference. Waves produced by coherent sources are therefore coherent. Coherence is used to indicate two waves that have a constant phase difference. Fig. 1 Wavefronts connecting crests and troughs of waves from each source are drawn. When two waves travel along paths of unequal length to meet at a point (eg. Point C), there is a path difference between the waves from their respective sources to that point. Key term: Path difference Path length is the distance travelled by a wave from its source to a point. When waves from two sources meet at a point, the difference in their respective path lengths is called path difference. In the figure above, the path difference for the waves to meet at C is 6λ - 4λ = 2λ. At which points in Fig. 1 are the path differences 0, ½ λ, λ, 3/2 λ or 2λ? This path difference can be used to tell the phase difference of the waves when they arrive at the point. Key term: Phase difference • A measure of how much one wave is out of step with another . A phase difference of one cycle corresponds to 360 or 2 radians • Two waves are said to meet in phase when they have a phase difference of 2n, where n = 0, 1, 2, … Two sources or waves do not have to be in phase to have a constant phase difference. Note that it is incorrect to use “same phase difference” to describe coherent sources which has “constant phase difference”.

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