TJC 10 Waves

Student’s copy 2025 Temasek Junior College Mrs Poon SC Unit 10: Wave Motion Learning Outcomes Candidates should be able to: (a) show an understanding of and use the terms displacement, amplitude, period, frequency, phase difference, wavelength and speed (b) deduce, from the definitions of speed, frequency and wavelength, the equation v = f λ (c) recall and use the equation v = f λ (d) show an understanding that energy is transferred due to a progressive wave (e) recall and use the relationship, intensity ∝ (amplitude)2 (f) show an understanding of and apply the concept that wave from a point source and travelling without loss of energy obeys an inverse square law to solve problems (g) analyse and interpret graphical representations of transverse and longitudinal waves (h) show an understanding that polarisation is a phenomenon associated with transverse waves (i) recall and use Malus’ law (intensity ∝ cos2θ) to calculate the amplitude and intensity of a plane polarised electromagnetic wave after transmission through a polarising filter (j) determine the frequency of sound using a calibrated oscilloscope (k) determine the wavelength of sound using stationary waves. *(l) explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes *(m) show an understanding of experiments which demonstrate stationary waves using microwaves, stretched strings and air columns *learning outcomes of topic of Superposition

2 1 INTRODUCTION A wave is initiated by a vibrating object (the source) and it travels away from the object. The particles of the medium vibrate about their rest position at the same frequency as the source. The wave transfers energy between two points in a medium without any net transfer of the matter or material in the medium. 2 PROGRESSIVE WAVES LO(d) A progressive wave transfers energy from one place to another without the transfer of medium. Sound waves, waves on a string, electromagnetic waves etc are progressive waves by nature. Mechanical waves require a medium, such as string or air, to travel; whereas electromagnetic waves can travel through a vacuum, without any medium. (Read Appendix A for EM waves). Progressive waves can be further classified into transverse and longitudinal waves. 2.1 Transverse Waves Transverse waves are waves in which the oscillation of the particles of the medium is perpendicular to the direction of energy transfer. The passage of a wave through a medium can be demonstrated using a 'slinky' spring. If the spring is subjected to a repeated up and down motion, a transverse wave is set up. The individual parts of the spring oscillate in the vertical plane while the wave transfer energy horizontally along the spring as shown in the figure above. Other examples of transverse waves are waves on strings, seismic waves , water waves and electromagnetic(EM) waves. 2.2 Longitudinal Waves Longitudinal waves are waves in which the oscillation of the particles of the medium is parallel to the direction of energy transfer. If the slinky spring is repeatedly given a push and a pull, a longitudinal wave is created. The individual parts of the spring move back and forth about their equilibrium positions, causing a series of compressions and rarefactions. energy transfer

3 Compressions occur where the loops of the spring are closer together than at equilibrium while rarefactions appear where the loops are farther apart. All oscillations are parallel to the direction of the energy transfer in a longitudinal wave. Examples of longitudinal waves are sound waves and longitudinal waves on a slinky spring. 3 WAVE TERMINOLOGY LO(a),(b),(c) Term Symbol Unit Definition displacement x or y m The distance in a specified direction from the equilibrium position amplitude A m the maximum displacement of any particle/point on the wave from its equilibrium position wavelength  m The distance between any two successive particles/points on the wave that are in phase (e.g. the distance between successive crests or troughs) period T s The time taken for one complete oscillation of a particle/point in a wave (or the time taken for the wave to travel through one wavelength) frequency f Hz or s-1 The number of oscillations(or cycles) per unit time of a point in a wave wave speed v or c m s-1 The distance travelled by the wave per unit time Worked Example 1: Derive the wave equation v = f Solution: By defintition, speed = By definition, in one period T, the distance travelled by the wave is one wavelength . Hence speed v = Since frequency f = 1/T  v = f energy transfer

4 4 GRAPHICAL REPRESENTATION OF WAVES LO(g) There are two types of graph s that are generally used when describing waves . They are displacement–distance and displacement–time graphs. The graphs are sinusoidal (meaning sine of cosine graphs) because the particles in the wave are vibrating in s.h.m.. 4.1 Displacement-distance graph This shows how the displacements of the particles (or points) in the wave vary with the distance from the source at a particular instant. Such a graph is like a snapshot of the wave. This graph can be used to determine the wavelength (distance between successive crests or successive troughs). For longitudinal waves such as sound waves, the displacement of the particles is parallel to the motion, so a wave profile is more difficult to draw. But a displacement-distance graph identical to that for transverse waves can be drawn with positive displacements to the right of the equilibrium position and negative displacements to the left. For longitudinal sound waves, the regions of high pressure/density are called compressions and the regions of lower pressure/density are called rarefactions. The wavelength of a longitudinal wave is the distance between successive compressions, or the distance between successive rarefactions. wavelength  distance displacement 0 amplitude A wavelength  crest trough /distance rarefaction compression rarefaction Particles in equilibrium positions Positions of particles at time t rarefaction rarefaction compression

5 4.2 Displacement-time graph This shows how the displacement of a single particle (or point) in the wave varies with time. It is the graph of a particle performing s.h.m. with the same frequency as the wave. From this graph, the period of the wave motion can be determined (interval between successive crests or successive troughs on the graph). 4.3 Graphical representation of a progressive wave Using a sequence of displacement –distance graphs can provide a good understanding of how the position of an individual particle/point changes with time in a progressive wave. In the figure below, graph 1 represents a progressive wave moving to the right, the arrows shows the direction of movement of particles at that instant. The second graph 2, represents the position of the same wave a short time later. Notice that the crest in Graph 2 has shifted to the right, showing that the wave is travelling to the right. Worked Example 2 The displacement-distance and displacement-time graphs are for a water wave produced in a ripple tank. What is the speed of the water wave? A 0.1 m s-1 B 0.2 m s-1 C 10 m s-1 D 20 m s-1 Graph 1 Graph 2 period T time displacement 0 amplitude A /direction of travel

6 5 PHASE DIFFERENCE