RI Chap 10 Wave Motion Lecture Notes

10 WAVE MOTION H2 Physics 9478 Content Page 10.1 Progressive Waves 2 10.2 Intensity of a Wave 10 10.3 Transverse and Longitudinal Waves 14 10.4 Polarisation 17 10.5 Appendix 20 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 λ= . (d) recall and use the equation vf λ= . (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 polarisation is a phenomenon associated with transverse waves. (j) recall and use Malus’ law (intensity ∝ 2cos θ ) to calculate the amplitude and intensity of a plane polarised electromagnetic wave after transmission through a polarising filter.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 2 10.1 Progressive Waves A wave can be described as a disturbance that travels through a medium from one location to another location. Waves can be considered as an energy transport phenomenon because energy is transferred from one point to another some distance away in the direction of wave propagation. This chapter will focus on progressive waves.  Wave Terminologies Displacement x of a particle is the distance in a specific direction of a particle of a wave from its equilibrium position. Amplitude 0x or A is the magnitude of the maximum displacement of a particle in the wave from its equilibrium position. Period T is the time taken for a particle of a wave to complete one oscillation. Frequency f of a wave is the number of oscillations made per unit time. Wavelength λ of a wave is the distance between two consecutive points which are in phase. Speed v of a wave is the speed at which the wave shape (or wave profile) moves. Phase φ of a wave is an angle that gives a measure of the fraction of a cycle that has been completed by an oscillating particle or by a wave. Phase difference φ∆ between two particles in a wave or between two waves at a point is a measure of the fraction of a cycle which one is ahead of the other. Wavefront is a line or surface joining points on a wave that are in phase. The wave travels in a direction perpendicular to the wavefront. 1 T f = , unit: hertz (Hz) One oscillation cycle is equival ent to a phase angle of 2 radπ . Progressive Wave A progressive wave transports energy from one point to another in the direction of wave propagation.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 3  Mechanical Waves and Electromagnetic Waves Mechanical waves are waves that require a medium to propagate. An example is a rope connected to an oscillatory source, producing waves that travel along the rope, as shown in Fig. 10.1(a). Electromagnetic (EM) waves do not require a medium to propagate, and hence are not mechanical waves. This is how EM waves, such as visible light, are able to travel from the Sun to reach the Earth through vacuum. Fig. 10.1(b) shows an EM wave travelling in the z direction, with perpendicular electric and magnetic fields in the x- and y directions. Fig. 10.1(a) Fig. 10.1(b)  Oscillations in waves In a progressive wave, particles oscillate about their equilibrium positions. The particles in the medium do not move along with the wave. Hence, a progressive wave transports energy from one point to another, but do not transport matter. In the video (scan QR code to view) , we can observe how the wave travels to the right, but the particles in the video do not move in the horizontal direction – they oscillate vertically about their equilibrium positions, and not in the direction of the wave propagation. In an electromagnetic (EM) wave, there is no particle involved in oscillations. Instead, the electric and magnetic fields of the EM wave oscillate perpendicularly to each other. Illustration of how particles in a progressive wave oscillate

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 4  Graphical Representation of Waves Waves can be represented graphically in two ways: Displacement-distance graph shows the displacement of ALL particles in a wave at a particular instant of time. Displacement-time graph shows the displacement of ONE particle (P) in a wave over time. This is a snapshot of a wave. displacement y 0 P wavelength λ amplitude A distance xλ displacement y 0 period T time t amplitude A T 2T

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 5 Example 1 The diagram shows the variation with distance x of the displacement y of a transverse wave at a particular instant. The wave is travelling to the right. The frequency of the wave is 12.5 Hz. At the instant shown, the displacement is zero at the point P. Determine the shortest time to elapse before the displacement is zero at point Q. Hint: Think about the distance between point P and point Q in terms of the wavelength of the wave. [Solution]  Speed of a Progressive Wave The particles of a wave do not move with the propagation of the wave. They only oscillate about their equilibrium positions with different phases within one wavelength. The result is that a waveform is created that moves in the direction of energy transfer. In a time of one period T, the waveform moves a distance of one wavelength λ. The speed of the wave distance timev T λ= = Since 1f T= , vf λ= x y 0 P Q

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page| 6  Phase and Phase Difference The phase of a particle in oscillation is the fraction of an oscillation cycle it is at relative to its starting displacement. The phase difference between two particles is how much one particle is “ahead” or “behind” the other as a fraction of an oscillation cycle at any given instant. It is typically measured in radian or degree. Consider the particles A, B, C & D in a wave (Fig. 10.2). All the particles are in simple harmonic motion about their equilibrium positions. The wave profile at the next instance is illustrated by the dotted line. Fig. 10.2 Refer to pg. 3 of Oscillations lecture note. displacement velocity acceleration mag. dir. mag. dir. mag. dir. A 0x up 0 - 2 0xω down B 0 - 0xω up 0 - C 0x up 0 - 2 0xω down D 0x down 0 - 2 0xω up Two particles in a wave oscillate in phase when they are at the same fraction of their oscillation cycle relative to their starting displacements. These particles have a phase difference of 0 rad or 0° . Particles that are at different fractions of an oscillation cycle are out of phase with one other. These particles have a non- zero phase difference. Two particles in a wave oscillate in anti-phase when there is a difference of 1/2 an oscillation cycle in their phase. These particles have a phase difference of radπ or 180° . If the starting displacement s of all particles are at their respective equilibrium positions, particles A and C, are both at 1/4 of their oscillation cycle.