UNIVERSITY OF GUYANA FACULTY OF NATURAL SCIENCES DEPART. OF MATH, PHYS & STATS PHY 110 – PHYSICS FOR ENGINEERS LECTURE 6 (THURSDAY, OCTOBER 6, 2011) 1

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 2

2.1 Wave Characteristics 3 Introduction: Wave Motion, in physics, mechanism by which energy is conveyed from one place to another in mechanically propagated waves without the transference of matter. At any point along the path of transmission a periodic displacement, or oscillation, occurs about a neutral position. The oscillation may be of air molecules, as in the case of sound traveling through the atmosphere; of water molecules, as in waves occurring on the surface of the ocean; or of portions of a rope or a wire spring.

2.1 Wave Characteristics 4 Introduction Cont’d: In each of these cases the particles of matter oscillate about their own equilibrium position and only the energy moves continuously in one direction. Microsoft ® Encarta ® 2007.

2.1 Wave Characteristics 5 What is a wave? a) It is a travelling disturbance. b) It is a means of transferring energy from one point to another without the transfer of matter. c) It is a disturbance of an equilibrium condition that propagates from one region of space to another with time. Wave Motion: This is the behaviour of particles that have been disturbed by a wave which is often periodic or cyclic.

2.1 Wave Characteristics 6 All waves exhibit the following characteristics: 1. Reflection: Bouncing or rebounding off a surface. 2. Refraction: Bending of waves on leaving medium. 3. Interference: Occupying same region of space with a constant phase difference. 4. Diffraction: Spreading of wave fronts. 5. Superposition: Occupying same region of space with resulting disturbance the sum of the two waves.

2.1 Wave Characteristics 7 Reflection: This is the bouncing off of or rebounding of a wave when it is incident on a surface. Whenever a wave is incident on a surface, it may be reflected, transmitted or absorbed. Considering the portion reflected, experiments have shown that two laws hold.

2.1 Wave Characteristics 8 Laws of Reflection: 1. The incident wave, the reflected wave and the normal at the point of incident are all in the same plane. 2. The angle of incidence and the angle of reflection are equal.

2.1 Wave Characteristics 9 The Usborne Illustrated Dictionary of Physics, pg 36.

2.1 Wave Characteristics 10 The Usborne Illustrated Dictionary of Physics, pg 36.

2.1 Wave Characteristics 11 Physics for the IB Diploma by Tim Kirk, pg159.

2.1 Wave Characteristics 12 Laws of Reflection: Physics for the IB Diploma by Tim Kirk, pg159.

2.1 Wave Characteristics 13 Refraction: This is the bending of a wave when it moves from one medium to another of differing densities. In the case of light, the media has differing optical densities. As a consequence of refraction, there is a change in the direction of travel, wave velocity and wavelength. Experiments with light show that two laws hold: 1. The incident wave, the refracted wave, and the normal to the boundary at the point of incidence all lie in the same plane.

2.1 Wave Characteristics 14 2.This important law, named after Dutch mathematician Willebrord Snell, states that the product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium. Microsoft ® Encarta.

2.1 Wave Characteristics 15 The Usborne Illustrated Dictionary of Physics, pg 37.

2.1 Wave Characteristics 16 The Usborne Illustrated Dictionary of Physics, pg 37.

2.1 Wave Characteristics 17 The Usborne Illustrated Dictionary of Physics, pg 37.

2.1 Wave Characteristics 18 Interference: This occurs whenever two or more waves meet in space that there is a constant phase relationship between them and they are of similar amplitudes. In fact the waves must be coherent, i.e. they have the same frequency, wavelength and speed (velocity). Thus wave may interfere constructively or destructively.

2.1 Wave Characteristics 19

2.1 Wave Characteristics 20 The Usborne Illustrated Dictionary of Physics, pg 38.

2.1 Wave Characteristics 21 Diffraction: This is the spreading of the wave whenever it passes through a slit (opening) that is comparable in dimension to it wavelength.

2.1 Wave Characteristics 22 The Usborne Illustrated Dictionary of Physics, pg 37.

2.1 Wave Characteristics 23 The Usborne Illustrated Dictionary of Physics, pg 37.

UNIVERSITY OF GUYANA FACULTY OF NATURAL SCIENCES DEPART. OF MATH, PHYS & STATS PHY 110 – PHYSICS FOR ENGINEERS LECTURE 7 (FRIDAY, OCTOBER 14, 2011) 24

2.1 Types of Waves 25 Types of Waves: Waves are caterigorised based on 1. Need of a medium for propagation. Mechanical waves require a medium but electromagnetic waves do not. 2. Behaviour of particles disturbed by the wave i.e. the direction of the displacements in relation to the direction of the motion of the wave itself. 3. Dimensions of Propagation. 1-D, 2-D & 3-D waves.

2.1 Types of Waves 26 Longitudinal Waves: The longitudinal wave is always mechanical because it results from successive compressions (state of maximum density and pressure) and rarefactions (state of minimum density and pressure) of the medium. Sound waves typify this form of wave motion. Microsoft ® Encarta ® 2007.

2.1 Types of Waves 27 Transverse Waves: Another type of wave is the transverse wave, in which the vibrations are at right angles to the direction of motion. A transverse wave may be mechanical, such as the wave projected in a taut string that is subjected to a transverse vibration (see Fig. 2); or it may be electromagnetic, such as light, X ray, or radio waves (see Radio; X Ray). Microsoft ® Encarta ® 2007.

2.1 Types of Waves 28

2.1 Types of Waves 29 Transverse wave: Electromagnetic Wave

2.2 Wavelength, Frequency & Velocity 30 Properties of Waves: All waves possess: 1. Amplitude A: This is the maximum positive displacement of a particle that has been disturbed by a wave. Units: meters - m. 2. Wavelength λ: This is the distance between successive crests or troughs. Units: meters - m. 3. Frequency f: This is the number of cycles or oscillations a wave executes per second. Units: Hertz (Hz) or Cycles per second.

2.2 Wavelength, Frequency & Velocity 31

2.2 Wavelength, Frequency & Velocity 32 Properties of Waves: All waves possess: 1. Period T: This is the time taken for a wave to complete one cycle or oscillation. Units: Seconds. 2. Speed/Velocity V: This is the distance a wave travels per unit time. Units: ms -1

2.3 Graphical and Mathematical Description 33 Introduction: All waves are generally cyclic, that is, repetitive. Thus they may be represented by some trigonometric function. In most cases, that function is either Sine or Cosine wave function. These function gives a relationship between the following quantities: 1. Displacement of a particle disturbed by a wave. 2. Distance of the disturbed particle from the source of the wave. 3. Time.

2.3 Graphical and Mathematical Description 34 Wave Equations: They are three standard wave equations:

2.3 Graphical and Mathematical Description 35

2.3 Graphical and Mathematical Description 36 Inverse Square Law: It states that the intensity of a wave is inversely proportional to the square of the distance from the source of that wave.

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 37

38 END OF LECTURE