EJC Physics H212b Superposition 2023 1. Notes (full)

9749(202 3) H2 Physics H212 Superposition – Notes Page 1 of 15 H2 Topic 12b – Superposition A Water Spouting Bowl is a dramatic demonstration of standing waves. When damp hands run over the handles under the right conditions, resonance occurs and standing waves form around the circular bronze bowl, res ulting in water ejecting at antinodes around the rim. Content (H211 Waves) • Determination of frequency and wavelength of sound waves Learning Objectives: Candidates should be able to: (k) determine the wavelength of sound using stationary waves Content (H212 Superposition) • Stationary waves Learning Outcomes Candidates should be able to: (c) show an understanding of experiments which demonstrate stationary waves using microwaves, stretch strings and air columns (d) explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes 12.4 Stationary Waves In H211 Waves , we learnt that a progressive wave transports energy. Here, we shall see how the superposition of two waves can cause interference such that energy is localised (confined within a region) despite wave motion. The waves formed are called stationary waves or standing waves. The wave is stationary because the wave profile does not propagate although the particles still oscillate. Because the wave profile does not move, energy is not transmitted along the wave. wave 1 wave 2 resultant The resulting standing wave has a wave profile that visually moves up and down. We can also think of it as two waves transporting energy in opposite directions, so “net -net” the energy no longer is transported and hence is “stationary”.

9749(202 3) H2 Physics H212 Superposition – Notes Page 2 of 15 12.4.1 Region of Overlap For the phenomena that we have seen earlier in H212a, we apply the Principle of Superposition at a particular location on the screen. For standing waves, we apply the principle over the entire length over which two waves meet and overlap. 12.4.2 Formation of Stationary Waves When asked to explain the formation of stationary waves in a particular set up, with the necessary features mentioned above in mind, be sure to describe: • how 2 progressive waves of the same type are generated such that they are the same amplitude, frequency, wavelength and speed • how the 2 waves are travelling in opposite directions towards each other • where the 2 waves meet and overlap source 1 source 2 bright fringe waves superpose here at a spot on the screen wave 1 wave 2 resultant waves superpose across whole length A stationary wave is formed when two waves of the same type, same amplitude, same frequency, wavelength and speed, travelling in opposite directions towards each other, meet and overlap to superpose across a length. For A-Level H2 Physics, standing waves are almost only 1D such as on a string or along a column. In real life, there are stationary waves on 2D surfaces (e.g. drum skins) and in 3D structures.

9749(202 3) H2 Physics H212 Superposition – Notes Page 3 of 15 Example 20 Two speakers connected in parallel to the same signal generator are directed facing each other to investigate stationary waves. Explain how a stationary wave is formed. Solution Both speakers output progressive longitudinal sound waves in opposite directions that have the same speed as they travel in the same medium of air and have the same wavelength and frequency as they are connected to same signal generator. Both waves meet and overlap to superposes along the line joining the two speakers Example 21 In the set up below, explain how the stationary wave is formed in the string. Solution oscillator sends out progressive transverse wave in string towards pulley wave reflects at the end of the string where pulley is, back towards oscillator reflected wave has same speed, frequency and wavelength but travels in opposite direction meets and overlap with wave from oscillator to superpose along the string between the oscillator and the smooth pulley Note: for both E.g. 20 and 21, check against the features mentioned at bottom of page 2. signal generator speaker speaker bench top mechanical oscillator mass hanger smooth pulley string

9749(202 3) H2 Physics H212 Superposition – Notes Page 4 of 15 12.4.3 Reflection of Progressive Waves at Boundary Conditions Stationary waves are often (but not always as per Example 20) formed when an original wave meets and overlaps with a reflected wave travelling in the opposite direction because the reflection preserves the type, amplitude, speed, frequency and wavelength. Boundaries are where the reflections take place. Different boundary conditions result in different resultant amplitudes (from the superposition of original and reflected waves) at the boundary. Boundaries can be either fixed ends or free ends. type of wave physical condition at boundary boundary type resultant displacement at boundary phase change of reflected wave transverse waves on stretched string loop that slides without friction free end maximum amplitude original and reflected waves meet in-phase 0φ∆= tied to fixed end fixed end no displacement original and reflected waves meet in anti-phase or 180 φπ∆= ° transverse microwaves in air or vacuum microwaves reflect off a sheet of metal fixed end no displacement original and reflected waves meet in anti-phase or 180 φπ∆= ° longitudinal sound waves along a tube sound waves travel down a tube and reflect at open end free end maximum amplitude original and reflected waves meet in-phase 0φ∆= sound waves travel down a tube and reflect at closed end fixed end no displacement original and reflected waves meet in anti-phase or 180 φπ∆= ° For Example 20, the 2 waves meet and overlap into each other in free space. There are no boundary conditions in free space so a standing wave will always be formed. For Example 21, the boundary conditions are such that the two ends must be fixed ends along the string. Therefore, standing waves can only be formed when the wavelength of the waves can fit into the boundaries and satisfy the boundary conditions. microwave transmitter metal plate sound is longitudinal so it is physically impossible to oscillate into closed wall

9749(202 3) H2 Physics H212 Superposition – Notes Page 5 of 15 12.4.4 Properties of Stationary Waves When the two identical progressive waves meet and overlap with each other while travelling in opposite directions, some points will never move and some others will move the most. The resultant waveform has the following features: 1. Wave profile does not propagate. 2. Wave profile has a characteristic pattern of nodes and antinodes • node: a point where the amplitude is constantly zero • antinode: a point of maximum amplitude 3. Every particle of the wave, except nodes, oscillates with same frequency (same frequency as the incident or reflected progressive waves). 4. Distance between adjacent nodes (or adjacent antinodes) is 1 2λ . 5. Between two adjacent nodes, every particle oscillates in-phase. 6. Particles in adjacent inter-nodal segments oscillate in anti-phase. 7. Particles that are of same distance away from a node have the same amplitude. 8. The speed in vf λ= is the speed of the incident or reflected progressive wave. wave 1 resultant wave 2 nodes nodes nodes nodes nodes antinodes antinodes antinodes Tip: you can consider remembering node as no-displacement. displacement distance antinode antinode antinode node node Within this distance, all particles in-phase and reach individual differing amplitudes at same time. Particles in adjacent inter -nodal segments oscillate in anti -phase – as one reaches positive