HCI 09 Waves Lecture Notes

Chapter 9 Wave Motion Left: a 3D image viewed without glasses on the LG set; right: the same image viewed through 3D glasses shows noticeable ghosting and visible horizontal bands. (Photo taken at closer-than-normal viewing distance.) Source: Consumer Reports.org

Hwa Chong Institution (College) H2 Physics C1 2023 I Topic 9: Wave Motion Syllabus 9749 Content  Progressive waves  Transverse and longitudinal waves  Polarisation  Determination of frequency and wavelength of sound waves 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 vf  . (c) recall and use the equation vf  . (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 a 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. * To be covered in Topic 10 Superposition.

Hwa Chong Institution (College) H2 Physics C1 2023 II Table of Contents Syllabus 9749 ................................ ................................ ................................ ............................ I 9.1 Introduction ................................ ................................ ................................ ........................ 1 9.2 Classification of Waves ................................ ................................ ................................ ...... 1  Transverse and Longitudinal Waves ................................ ................................ .......... 4  Progressive Waves and Stationary Waves ................................ ................................ 1 9.3 Basic Terminology................................ ................................ ................................ .............. 6  Sinusoidal Waves ................................ ................................ ................................ ..... 6 9.4 Graphical Representation of Waves ................................ ................................ ................. 12  Graph of Displacement (y) vs. Position (x) ................................ ............................... 12  Graph of Displacement (y) vs. Time (t) ................................ ................................ .... 14 9.5 Phase and Phase Difference ................................ ................................ ............................ 16 9.6 Energy Transmitted by a Wave ................................ ................................ ........................ 19  Intensity of a Wave ................................ ................................ ................................ . 19  Intensity of a Wave from Point Source or Spherical Source ................................ ...... 20 9.7 Polarisation of Waves ................................ ................................ ................................ ...... 21 i. Light Passing Through Two Polarisers ................................ ......................... 23 Appendices ................................ ................................ ................................ ............................ 26  Appendix A: Function Generator and Cathode Ray Oscilloscope (C.R.O) ................. 26 i. Function Generator ................................ ................................ ..................... 26 ii. Cathode Ray Oscilloscope ................................ ................................ ........... 27  Appendix B: 3-D films and Polarization ................................ ................................ .... 28  Appendix C: Polarisation by Absorption ................................ ................................ ... 29 Tutorial 9 Wave Motion ................................ ................................ ................................ .......... 30  Self-Review Questions ................................ ................................ ........................... 30  Discussion Questions ................................ ................................ ............................. 34

Hwa Chong Institution (College) H2 Physics C1 2023 -1- 9.1 Introduction Consider a rope that is held under tension. If we give the left of the rope a small wiggle, a pulse is formed (called the waveform) which can be seen to travel along the length of the rope (Fig. 9.1.1). When the waveform travels down the rope, there is a transfer of energy and momentum from one end of the rope to the other. However each section of the rope only vibrates up and down about an equilibrium position --- no section of the rope actually travels from one end to the other. Fig. 9.1.1 Wave pulse travelling down the rope 9.2 Classification of Waves Waves can be categorised by three broad properties (Fig. 9.2.1): (i) the type of the wave, (ii) the mode of vibration of the wave, and (iii) the motion of the wave. Fig. 9.2.1 Classifications of Waves For example, a sound wave can be characterised as mechanical in nature, longitudinal in terms of its displacement and can be either progressive or stationary. (iii) Motion Type

Hwa Chong Institution (College) H2 Physics C1 2023 -2- Mechanical Waves Mechanical waves are created when part of a physical medium is disturbed. The disturbance spreads through the medium distributing energy to points far from the original disturbance. All mechanical waves therefore require a medium for propagation.1 The speed of wave propagation depends on the medium (specifically both its inertial and elastic properties). Sound waves, waves in ropes, water waves and seismic waves are all examples of mechanical waves. Electromagnetic (EM) waves Electromagnetic (EM) waves consist of mutually perpendicular time -varying electric field ( E  ) and magnetic field ( B  ) oscillating perpendicularly to the direction of wave travel (Fig. 9.2.2). Fig. 9.2.2 The E-field and B-field are mutually perpendicular to each other and both fields are also perpendicular to the direction of wave travel. Characteristics of EM Waves:  All EM waves are transverse in nature, i.e. the planes of oscillation of the electric and magnetic fields are perpendicular to the direction of motion.  All EM waves are self-propagating and hence do not require a medium in which to travel . Unlike mechanical waves they can move through a vacuum but are also able to propagate through materials e.g. light through glass, X-rays through bone and radio waves through walls.  In vacuum, all EM waves travel at the same speed c known as the speed of light: c = 3.00 x 108 m s-1 The Electromagnetic Spectrum Common examples of electromagnetic waves include visible light, ultraviolet light, radio wave, microwaves and x-rays. Fig. 9.2.3 shows the electromagnetic spectrum and relative positions of these EM waves on the spectrum. Fig. 9.2.3 The electromagnetic spectrum. 1 Propagation of mechanical waves is possible due to the restoring forces produced upon deformation; Sound waves, which rely on oscillations of molecules of the medium resulting in pr