JPJC 2026 Waves Motion Notes Tutor

2026/JPJC/PHYSICS/9478 1 JURONG PIONEER JUNIOR COLLEGE 9478 H2 PHYSICS WAVE MOTION Content • Properties of waves • Energy transfer by progressive waves • Polarisation Learning Outcomes Candidates should be able to: (a) show an understanding that mechanical waves involve the oscillations of particles within a material medium, such as a string or a fluid, and electromagnetic waves involve the oscillations of electromagnetic fields in space and time (b) show an understanding of and use the terms displacement, amplitude, period, frequency, phase, phase difference, wavelength and speed (c) deduce, from the definitions of speed, frequency and wavelength, the equation vf = (d) recall and use the equation vf = (e) analyse and interpret graphical representations of transverse and longitudinal waves with respect to variations in time and position (space) (f) show an understanding that energy is transferred due to a progressive wave without matter being transferred (g) recall and use the term intensity as the power transferred (radiated) by a wave per unit area, and the relationship intensity  (amplitude)2 for a progressive wave (h) show an understanding of and apply the concept, that the intensity of a wave from a point source and travelling without loss of energy obeys an inverse square law to solve problems (i) show an understanding that p olarisation is a phenomenon associated with transverse waves (j) 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.

2026/JPJC/PHYSICS/9478 2 1 What is a wave? (a) show an understanding that mechanical waves involve the oscillations of particles within a material medium, such as a string or a fluid, and electromagnetic waves involve the oscillations of electromagnetic fields in space and time. Wave motion is the transmission of energy from one place to another through a material or in a vacuum, without the physical transfer of any material between the points. • The source of any wave is a vibration or oscillation. • It is the energy that is transferred along the direction of propagation, and not the particles. • Each particle oscillates about its equilibrium position in the same way as its neighbour. • The particles oscillate about their equilibrium positions while the wave moves along the direction of propagation at the same time as shown in Fig. 1. Fig. 1 Particles oscillate vertically A progressive wave is one where the wave profile moves along the direction of propagation and energy is transferred from the source to other points further away without matter being transferred. 1.1 Mechanical Waves A mechanical wave is a wave that involves the oscillation of particles of a material medium about their equilibrium positions. Key Characteristics • a material medium is required (e.g. solid, liquid, or gas) • cannot propagate in vacuum • energy transfer occurs through interactions between neighbouring particles • examples: waves on a stretched string, water surface waves, sound waves in air 1.2 Electromagnetic Waves An electromagnetic (EM) wave is a wave consisting of oscillating electric and magnetic fields that propagate through space. Key Characteristics • no material medium required • can propagate through vacuum • consist of mutually perpendicular electric field and magnetic field oscillat ing perpendicular to the direction of wave propagation wave velocity v

2026/JPJC/PHYSICS/9478 3 • is a transverse wave with electric and magnetic fields varying sinusoidally with time • For EM waves, the speed c, frequency f, and wavelength  , is related by  c = f EM radiation carries energy and momentum, which may be imparted when it interacts with matter. EM waves travel with a speed of 813.0 10 m sc −= in vacuum (c is the speed of light in vacuum). • The electromagnetic spectrum classifies electromagnetic waves according to the frequencies (or wavelengths), into 7 broad categories - radio waves, microwaves, infra-red waves, visible light, ultraviolet waves, x-rays, and gamma rays. Visible light has a range in wavelength from about 400 to 700 nm as shown in Fig. 2. Fig. 2 The wavelength values for visible light

2026/JPJC/PHYSICS/9478 4 2 Describing Waves (b) show an understanding of and use the terms displacement, amplitude, period, frequency, phase, phase difference, wavelength and speed. (c) deduce, from the definitions of speed, frequency and wavelength, the equation vf = (d) recall and use the equation vf = . 2.1 Basic Terminology Fig. 3 shows the different parts of a wave profile. • The crest is the highest point on a wave while the trough is the lowest point. Fig. 3 Parts of a wave profile Physical quantity Description displacement y / m the distance of a particle from its equilibrium position in a specified direction amplitude A / m the magnitude of the maximum displacement of an oscillating particle in a wave from its equilibrium position wavelength λ / m the distance between any two successive points on the wave which are in phase (e.g. between two crests or two troughs) period T / s the time taken for a particle of the wave to complete one oscillation frequency f / Hz the number of oscillations made by a particle of the wave per unit time 1f T= 2.2 Wave Velocity Wave velocity refers to the speed at which the waveform travels in the direction of propagation. For a wave that travels with a constant speed, the distance travelled by the wave is the wavelength  when the time taken is one period T. amplitude, A crest trough wavelength, λ displacement, y

2026/JPJC/PHYSICS/9478 5 Since speed is defined as the distance travelled per unit time, the velocity of the wave, v is v = T  = f  Note: • Wave velocity refers to the speed at which the energy is transmitted, and not the speed of the particles of the medium in the wave. • The speed of a wave depends on the medium in which the wave travels. • When a wave passes from one medium to another, the frequency of the wave remains constant, while the wavelength changes, hence the wave velocity changes. 2.3 Wave Representation 2.3.1 Wavefronts Wave can be represented in various ways depending on how closely we look at it. Fig. 4 A wave moving from left to right Wavefront is a line or surface joining points on a wave that are in phase. The wave travels in a direction that is perpendicular to the wavefront. • They move outwards or away from the wave source. • The arrows drawn perpendicularly to the wavefronts indicate the direction of the wave / energy propagation. Fig. 4.1 Plane wavefronts Fig. 4.2 Circular wavefronts

2026/JPJC/PHYSICS/9478 6 2.3.2 Displacement–Distance Graph If we take a snapshot at a particular time instant of a wave, the particles along the wave are at different “stages” of oscillation (e.g. up and down) about their equilibrium positions. This is represented by the displacement-distance graph of the wave as shown in Fig. 5. Fig. 5 Displacement-distance graph of a wave at an instant in time 2.3.3 Displacement–Time Graph If we look at only a single particle along a wave, we will observe that it oscillates (e.g. up and down) about an equilibrium position. Fig.6 shows how the displacement of this particle changes with time. Fig. 6 Displacement-time graph of a particle along a wave • Each particle in a wave exhibits simple harmonic motion. Displacement–distance ( y–x) graph shows the displacement y of all particles along the path of propagation ( at various distances x away from the source ) at an instant in time. displaceme