2022-12-7 4.1 Oscillations waves 4.1 Oscillations 4.2 Travelling waves 4.3 Wave characteristics 4.5 Standing waves 4.1 Oscillations • Simple harmonic motion (SHM) ØConditions 1. there is a fixed equilibrium position 2. when the particle is moved away from equilibrium, the acceleration of the particle is both proportional to the amount of displacement and in the opposite direction to it 4.1 Oscillations • Simple harmonic motion (SHM) Øpendulum spring-mass system 4.1 Oscillations • • • • • Simple Harmonic Motion (SHM) is defined as an oscillation where .. A. acceleration is proportional to the displacement from the centre. B. acceleration is proportional to the speed of the oscillation. C. acceleration is proportional to the velocity of the oscillation. D. acceleration is proportional to the mass of the system. l A large pendulum swings from the left to the right in 2 seconds. The frequency of the pendulum is: • A. 0.25 Hz • B. 0.5 Hz. • C. 2 Hz • D. 4 Hz 4.2 Travelling waves • A travelling wave is a continuous disturbance in a medium characterized by repeating oscillations. Energy is transferred by waves. Matter is not transferred by waves. The direction of a wave is defined by the direction of the energy transfer. 1 2022-12-7 4.2 Travelling waves 4.2 Travelling waves ØTransverse and longitudinal waves 4.2 Travelling waves ØTransverse and longitudinal waves Transverse wave Longitudinal wave The direction of oscillation is perpendicular to the direction of the wave The direction of oscillation is parallel to the direction of the wave 4.2 Travelling waves ØTransverse and longitudinal waves Transverse wave Longitudinal wave Transverse wave Longitudinal wave Example: l Water waves Example: A point with maximum positive displacement is called a crest. A region where particles are closed to each other is called a compression. A point with minimum displacement is called a trough. A region where particles are furthest apart from each other is called a rarefaction. l Wave produced in a spring l Wave in a string flicked up and down l Sound waves l Light (electromagnetic waves) l Earthquake P-waves 4.2 Travelling waves 4.2 Travelling waves ØThe nature of electromagnetic waves ØThe nature of sound waves All EM waves travel in vacuum at the same speed of 3*10^8m/s. EM waves are transverse waves. The speed of sound in 20 degrees Celsius dry air is approximately 343.2m/s. Sound waves are longitudinal waves. 2 2022-12-7 4.2 Travelling waves l The period of a wave is 0.5 s and the wave speed 100 ms-1. What is the frequency and wavelength of this wave? A. f = 2 Hz, λ = 50 m. B. f = 5 Hz, λ = 50 m. C. f = 2 Hz, λ = 20 m. D. f = 5 Hz, λ = 20 m. l Which of these answers correctly identifies longitudinal and transverse waves? 4.3 Wave characteristics 4.3 Wave characteristics 4.3 Wave characteristics Ø Wavefronts and rays Wavefronts: • Lines joining points which vibrate in phase. • Can be straight lines or curves. • The distance between successive wavefronts is the wavelength of the wave. Rays: • Lines which indicate the direction of wave propagation. • Rays are perpendicular to wavefronts. 4.3 Wave characteristics 4.3 Wave characteristics Ø Polarization by reflection 1. When light is transmitted across a boundary between two mediums with different refractive indexes, part of the light is reflected and the remaining part is refracted 2. The light reflected is partially polarized, meaning that it is a mixture of polarized light and unpolarized light. 3. The extent to which the reflected light is polarized depends on the angle of incidence and the refractive index of the two mediums. 4. The angle of incidence at which the reflected light is totally polarized is called the Brewster’s angle (ϕ) given by the equation i=ib reflected ray？refracted ray 3 2022-12-7 4.3 Wave characteristics Ø Polarizers and Analyzers 1. When a wave of amplitude A0 and intensity I0 passes through a polarising filter the intensity of the transmitted wave is ½I0. This means the transmitted wave amplitude is: Polarizer: • A polarizer is a sheet of material which polarizes light. • When unpolarized light passes through a polarizer, its intensity is reduced by 50%. Analyzer: • A polarizer used for this purpose is called an analyzer. • When polarized light passes through a polarizer, its intensity will be reduced by a factor dependent on the orientation of the polarizer. This property allows us to deduce the polarization of light by using a polarizer. 4.3 Wave characteristics A. A0 B. ½ A0 C. 1/√2 A0 D. ¼ A0 Malus’ Law 4.3 Wave characteristics 4.3 Wave characteristics 2-5 A light ray passes through 2 polarising filters. The first filter polarises the wave in a vertical plane. The second filter is rotated and the transmitted light I2 observed. 5 -8. A light ray passes through 2 polarising filters. The first filter polarises the wave in a vertical plane. The second filter is rotated and the transmitted light I2 observed. 2. Which of these gives the correct terms for the first and second filters? 3、The intensity of light incident on the first filter is I0. Which of these describes the intensity of light after the second filter I2 when it is held vertically or horizontally? 4.3 Wave characteristics 5 -8. A light ray passes through 2 polarising filters. The first filter polarises the wave in a vertical plane. The second filter is rotated and the transmitted light I2 observed. 4.3 Wave characteristics 5、Which of the 4 graphs below correctly shows the variation in intensity of the final observed beam I2 as the second filter is slowly rotated through 900 from its initial position? It is initially vertically aligned. 4、The final light intensity I2 is compared to I1 , the intensity after the first filter. What is the intensity of I2 when the angle between the two filters is 450, given that cos(450) = 1/√2? 4 2022-12-7 4.4 Wave behaviour 4.4 Wave behaviour Ø Reflection and refraction Reflection: Ø Reflection and refraction a fixed end Angle of incidence = Angle of reflection a free end Refraction: Reflection of waves from a fixed end is inverted. Reflection of waves from a free end is not inverted. n（refractive indexes） v1（the speed of the waves） λ1 （ wavelength） 4.4 Wave behaviour Ø Reflection and refraction 4.4 Wave behaviour Ø Diffraction through a single-slit and around objects Refraction: condition： the light ray propagates from a optically denser medium to an optically less dense medium. n1（The refractive index） θc（the critical angle ） 4.4 Wave behaviour Ø Interference patterns 4.4 Wave behaviour Ø Interference patterns Maximums form at constructive interference (the maximum is shown by 1-2) and minimums form at deconstructive interference (the first minimum is shown by 3-4). deconstructive constructive 5 2022-12-7 4.4 Wave behaviour Ø Double-slit interference Like single-slit diffraction, double-slit diffraction occurs via the same methods of interference and has a similar diffraction pattern. 4.4 Wave behaviour 1、 Total internal reflection will only occur if a wave is incident on a surface such as glass under certain conditions. Which of these best describes these conditions? A. The angle of incidence is greater than the critical angle, and the ray is travelling in air towards the glass. B. .The angle of incidence is less than the critical angle, and the ray is travelling in air towards the glass. C. The angle of incidence is greater than the critical angle, and the ray is travelling in glass towards the air. D. The angle of incidence is less than the critical angle, and the ray is travelling in glass towards the air. 4.4 Wave behaviour Ø Double-slit interference Path difference 4.4 Wave behaviour 3. A rope is tied and fastened to a pole, and two wave pulses are produced by moving the end of the rope up and down. The first pulse produced is weak, the second is much stronger and has a higher amplitude as shown below: The pulses are reflected on impact with the pole. Which of the following diagrams shows the reflected pulses correctly? 2、. Which of these is the best description of the critical angle of a medium? A. The angle of the incident ray when the refracted ray is at 900 to the normal line. B. The angle of the incident ray when the refracted ray is parallel to the normal line. C. The angle of the refracted ray when the incident ray is at 900 to the normal line. D. The angle of the refracted ray when the incident ray is at parallel to the normal line. 4.4 Wave behaviour 4-5、Water will refract light but also refract sound. The table below gives typical values for the speed of sound and light in sea water and in air. 4、Light and sound waves pass from air into water at an angle of incidence = 10o. Which of the answers in the table below gives the refracted angles for sound and light? 4.4 Wave behaviour 4-5、Water will refract light but also refract sound. The table below gives typical values for the speed of sound and light in sea water and in air. 5、If the refractive index of air is equal to 1.0, what is the refractive index of sea water for a light wave? 6 2022-12-7 4.4 Wave behaviour 6-7A light ray is incident on a glass block as shown.The refractive index of the air is 1.0, and 1.6 for the glass.The value of sin ( 300 ) is 0.5 6、As the light ray enters the glass and changes direction, some properties of the wave change. Which of these best describes the changes to the wave properties? 4.5 Standing waves Ø The nature of standing waves Standing waves (stationary) waves result from the superposition of two opposite waves which are otherwise identical. Energy is not transferred by standing waves. 4.5 Standing waves Ø Nodes and antinodes 4.4 Wave behaviour 6-7A light ray is incident on a glass block as shown.The refractive index of the air is 1.0, and 1.6 for the glass.The value of sin ( 300 ) is 0.5 7、Which of these formulas is equal to the angle of incidence, i? 4.5 Standing waves Ø Boundary conditions • Air particles can oscillate and create standing waves in pipes with open or closed ends. • Antinodes are positioned at open ends and nodes are positioned at closed ends. • Standing waves on a string is equivalent to that in a pipe which is closed on both ends (nodesnode). • Note that even harmonics do not exist for pipes with one closed end and one open end 4.5 Standing waves Ø Difference between standing waves and travelling waves • Positions along the wave which are fixed are called nodes (minimum) and those with the largest displacement are called antinodes (maximum). • For standing waves, the distance between adjacent nodes = the distance between adjacent antinodes = λ/2. 7 2022-12-7 4.5 Standing waves • A standing wave is typically formed by 2 waves meeting. Which of these statements about the 2 waves is correct? • A. The waves must be travelling in the same direction, and have different wavelengths. • B. The waves must be travelling in opposite directions, and have different wavelengths. • C. The waves must be travelling in the same direction, and have the same wavelength. • D. The waves must be travelling in opposite directions, and have the same wavelength. 4.5 Standing waves • 4. An antinode is a point where... • • • • A. The amplitude detected will be small, but not zero. B. The amplitude detected will be zero. C. The amplitude detected will be at a maximum. D. The amplitude detected will rise and fall constantly. 4.5 Standing waves • • • • • 2. What is the distance between consecutive nodes? A. ¼λ B. ½λ C. λ D. 2λ • • • • • 3. A node is a point where... A. The amplitude detected will be small, but not zero. B. The amplitude detected will be zero. C. The amplitude detected will be at a maximum. D. The amplitude detected will rise and fall constantly. 4.5 Standing waves 5-6A thin pipe of length 30cm is closed at one end. By blowing across the open end, different harmonics can be produced. • 5、What is the wavelength of the first harmonic ? A. 30 cm B. 40 cm C. 60 cm D. 120 cm 6、10. What is the wavelength of the third harmonic? A. 30 cm B. 40 cm C. 60 cm D. 120 cm 8
