Chapter 1: Waves

Damping and Resonance1 In an oscillating system such as the oscillation of a simple pendulum, the oscillation does not continue with the same amplitudes indefinitely.

Damping and Resonance2 The amplitude of oscillation of the simple pendulum will gradually decrease and become zero when the oscillation stops. The decrease in the amplitude of an oscillating system is called damping.

Damping and Resonance3 An oscillating system experiences damping when its energy is drained out as heat energy. (a) External damping of the system is the loss of energy to overcome frictional forces or air resistance.

Damping and Resonance(b) Internal damping is the loss of energy due to the extension and compression of the molecules in the system.

Damping and Resonance4 Damping in an oscillating system causes (a) the amplitude, and(b) the energy of the system to decrease.

Damping and Resonance4 Damping in an oscillating system causes (a) the amplitude, and(b) the energy of the system to decrease (c)the frequency, f does not change.

Damping and Resonance5 To enable an oscillating system to go on continuously, an external force must be applied to the system.

Damping and Resonance6 The external force supplies energy to the system. Such a motion is called a forced oscillation.

Damping and Resonance7 The frequency of a system which oscillates freely without the action of an external force is called the natural frequency.

Damping and Resonance8 Resonance occurs when a system is made to oscillate at a frequency equivalent to its natural frequency by an external force. The resonating system oscillates at its maximum amplitude.

Damping and Resonance9 The characteristics of resonance can be demonstrated with a Barton's pendulum system as shown in Figure 1.17.

Damping and Resonance(a) When pendulum X oscillates, all the other pendulums are forced to oscillate. It is found that pendulum B oscillates with the largest amplitude, that is, pendulum B resonates.

Damping and Resonance(b)The natural frequency of a simple pendulum depends on the length of the pendulum. Note that pendulum X and pendulum B are of the same length. Therefore, pendulum X causes pendulum B to oscillate at its natural frequency.

Damping and Resonance

10Hz8 Hz10 Hz9 Hz12 Hz10 Hz8 Hz12 HzDamping and Resonance10 Some effects of resonance observed in daily life:(a) The tuner in a radio or television enables you to select the programmes you are interested in. The circuit in the tuner is adjusted until resonance is achieved, at the frequency transmitted by a particular station selected. Hence a strong electrical signal is produced.

Damping and Resonance10 Some effects of resonance observed in daily life:(b) The loudness of music produced by musical instruments such as the trumpet and flute is the result of resonance in the air.

Damping and Resonance(c) The effects of resonance can also cause damage. For example, a bridge can collapse when the amplitude of its vibration increases as a result of resonance.

THE POWER OF RESONANCE CAN DESTROY A BRIDGE. ON NOVEMBER 7, 1940, THE ACCLAIMED TACOMA NARROWS BRIDGE COLLAPSED DUE TO OVERWHELMING RESONANCE. Damping and Resonance(d)Cracking of wine glass

Chapter 1: Waves1.2 Analysing Reflection of WavesRipple Tank

Ripple TankMain PartsFunctionsLampTo project the image of the water waves onto the white paper below the ripple tank

Ripple TankMain PartsFunctionsMotorThe vibrations of electric motor causes the plastic sphere to produce spherical waves, and the wooden bar to produce plane water waves

Ripple TankMain PartsFunctionsRheostatControls the frequency of the water waves produced

Ripple TankMain PartsFunctionsSpongeTo line the inside of the transparent tray to prevent reflection of water waves from the side of the tray.

Ripple TankMain PartsFunctionsStroboscopeTo freeze the image of the water waves

Ripple Tank

Ripple Tank1 A water wave is a type of transverse wave.

Ripple Tank2. When waves are produced on the surface of the water, a wave crest will act like a convex lens while a wave trough will act like a concave lens.

Ripple Tank3. Hence the crest focuses the light to form a bright fringe on the white screen below the ripple tank, and the trough diverges the light and forms a dark fringe on the white screen, as shown in Figure 1.21

Ripple Tank4. Each bright and dark fringe represents the wavefront of the water wave.

Ripple Tank5. A hand stroboscope can be used to freeze the motion of the water waves.

Ripple Tank6. When the fringe pattern on the white screen below the ripple tank is "frozen", the frequency of the water waves is given byf = n x p, where n = number of slits on the stroboscopep = rate of rotation of the stroboscopeRipple Tank7. The wavelength, , of the water wave is related by v = f.Reflection of Waves1 Reflection of a wave occurs when a wave strikes an obstacle. The wave undergoes a change in direction of propagation when it is reflected.

Reflection of Waves2 The incident wave is the wave before it strikes the obstacle, whereas the reflected wave is the wave which has undergone a change in direction of propagation after reflection.

i = angle of incidence;r = angle of reflection

Reflection of Waves3 The phenomenon of reflection of waves obeys the Laws of reflection where:(a) The angle of incidence, i, is equal to the angle of reflection, r.

Reflection of Waves3 The phenomenon of reflection of waves obeys the Laws of reflection where:(b) The incident wave, the reflected wave and the normal lie in the same plane which is perpendicular to the reflecting surface at the point of incidence.

Reflection of WavesExperiment 1.1 To investigate the reflection of plane wavesProblem statementWhat is the relationship between the angle of incidence and the angle of reflection of a water wave?

Reflection of WavesHypothesisThe angle of reflection is equal to the angle of incidence.

Reflection of WavesVariablesManipulated : Angle of incidence of the water wave Responding : Angle of reflection of the water wave Fixed : Depth of water, frequency of dipper

Reflection of WavesOperational definitionThe angle of incidence is the angle between the direction of propagation of incident wave and the normal. The angle of reflection is the angle between the direction of propagation of reflected wave and the normal.

Reflection of WavesApparatus/MaterialsRipple tank, plane reflector, a piece of white paper, wooden bar, lamp, motor, sponge and mechanical stroboscope.

Reflection of WavesProcedure1 A ripple tank is filled with water and is set up as shown in Figure 1.23. The tank is leveled so that the depth of water in the tank is uniform to ensure water waves propagate with uniform speed.

Reflection of WavesProcedure2All the inner surface of the ripple tank is lined with a layer of sponge to prevent reflection of the water waves from the edges.

Reflection of WavesProcedure3 The lamp above the tank is switched on and a large piece of white paper is placed below the tank.

Reflection of WavesProcedure4 A metallic plane reflector is placed at the centre of the tank. The motor with wooden bar attached is switched on to produce plane waves which propagate towards the reflector.

Reflection of WavesProcedure5The pattern (on the white paper) of the reflected waves produced by the vibrating wooden bar is observed with the help of a mechanical stroboscope. The incident waves and the reflected waves are sketched.

Reflection of WavesProcedure6 Steps 4 and 5 are repeated with the reflector repositioned so that the wave is incident at angles, i = 20, 30, 40, 50 and 60 on the reflector as shown in Figure 1.24.

Reflection of WavesResultsPattern of reflected wavesCharacteristic of waves(i)Angle of incidence, i = 0Angle of reflection, r = 0Wavelength, frequency and speed of wave do not change after reflection.Direction of propagation of water changes.

Reflection of WavesResults

Angle of incidence, i, ()2030405060Angle of reflection, r, ()2030405060Angle of incidence, i =Angle of reflection, r Wavelength, frequency and speed of wave do not change after reflection.Direction of propagation of water changes.Reflection of WavesConclusionThe angle of reflection is equal to the angle of incidence. The hypothesis is valid.Reflection of WavesExample 6A water wave of frequency 20 Hz appears stationary when observed through a stroboscope with 4 slits. What is the frequency of rotation of the stroboscope?Reflection of WavesExample 6SolutionFrequency of wave = Number of slits x Frequency of stroboscope 20 = 4 x f f = 5 HzReflection of WavesExperiment 1.2 : To investigate the reflection of sound wavesProblem statementWhat is the relationship between the angle of incidence and the angle of reflection of a sound wave?Reflection of WavesHypothesisThe angle of reflection is equal to the angle of incidence.Reflection of WavesVariables(a) Manipulated : Angle of incidence of the sound wave(b) Responding : Angle of reflection of the sound wave(c) Fixed : Distance of the stopwatch from the point of reflection on the wooden board

Reflection of WavesOperational definitionThe angle of incidence of the sound wave is the angle between the incident sound wave and the normal. The angle of reflection is the angle between the reflected sound wave and the normal.

Reflection of WavesApparatus/MaterialsTwo cardboard tubes, stopwatch, a slab of soft wood, a wooden board with a smooth surface and a protractor.

Reflection of WavesProcedure1 The apparatus is set up as shown in Figure 1.25.

Reflection of WavesProcedure2 The angle of incidence, i = 30 is measured with a protractor.3 The stopwatch is started.

Reflection of WavesProcedure4 The position of the cardboard tube B is adjusted until a loud ticking sound of the stopwatch is heard. 5 The angle of reflection, r at this position of the cardboard tube B is measured.

Reflection of WavesProcedure6 Steps 2 to 5 are repeated with the angles of incidence, i = 40, 50, 60 and 70. 7 The results are tabulated.

Reflection of WavesResultsAngle of incidence, i, ()3040506070Angle of reflection, r, ()3040506070Reflection of WavesDiscussionThe sound waves from the stopwatch experience a reflection after striking the wooden board. The slab of soft wood placed along the normal serves as a barrier to prevent the sound of the stopwatch from reaching the observer directly.

Reflection of WavesConclusionThe angle of incidence, i is equal to the angle of reflection, r. The laws of reflection are obeyed. The hypothesis is valid.Angle of incidence, i, ()3040506070Angle of reflection, r, ()3040506070Reflection of WavesExperiment 1.3: To investigate the reflection of lightProblem statementWhat is the relationship between the angle of incidence and the angle of reflection of a light ray?

Reflection of WavesHypothesisThe angle of reflection is equal to the angle of incidence.

Reflection of WavesVariables(a) Manipulated : Angle of incidence of light ray(b) Responding : Angle of reflection of the light ray (c) Fixed: Position of the plane mirror

Reflection of WavesOperational definitionThe angle of incidence of the light ray is the angle between the incident ray and the normal. The angle of reflection is the angle between the reflected ray and the normal.

Reflection of WavesApparatus/MaterialsPlane mirror, ray box, plasticine, protractor, white piece of paper and a sharp pencil.

Reflection of WavesProcedure1 A straight line, PQ is drawn on a sheet of white paper.

Reflection of WavesProcedure2 A normal line, ON is drawn from the midpoint of PQ.3 Using a protractor, lines at angles of incidence of 20, 30, 40, 50 and 60, with the normal, ON are drawn.

Reflection of WavesProcedure4 A plane mirror is erected along the line PQ.

Reflection of WavesProcedure5 A ray of light from the ray box is directed along the 20 line. The angle between the reflected ray and normal, ON is measured.

75Reflection of WavesProcedure6Step 5 is repeated with the angle of incidence, i of 30, 40, 50 and 60.7 The results are tabulated.

Reflection of WavesResults

The incident ray must be as narrow as possible to obtain a narrow and thin reflected ray. It can be done by adjusting the lens in the ray box (or a laser pen can be used instead).

Angle of incidence, i, ()2030405060Angle of reflection, r, ()2030405060Reflection of WavesConclusionThe angle of incidence, i is equal to the angle of reflection, r. The laws of reflection are obeyed. The hypothesis is valid.Applications of Reflection of waves in Daily LifeSafety(a) The rear view mirror and side mirror in a car are used to view cars behind and at the side while overtaking another car, making a left or right turn and parking the car. The mirrors reflect light waves from other cars and objects into the driver's eyes.

Applications of Reflection of waves in Daily LifeSafety(b) The lamps of a car emit light waves with minimum dispersion. The light bulb is placed at the focal point of the parabolic reflector of the car lamp so that the reflected light waves are parallel to the principal axis of the reflector. Parallel light waves have a further coverage.

Applications of Reflection of waves in Daily LifeDefenceA periscope is an optical instrument. It can be constructed using two plane mirrors for viewing objects beyond obstacles. The light waves from an object which is incident on a plane mirror in the periscope are reflected twice before entering the eyes of the observer.

Applications of Reflection of waves in Daily LifeMedicationThe concept of total internal reflection is used in optical fibres. Light entering one end of an optical fibre experiences multiple total internal reflections as it propagates through the whole length of the fibre before emerging at the other end. Optical fibres are used to examine the internal organs of patients, especially organs with internal cavities such as the colon and stomach, without operating on the patient.

Applications of Reflection of waves in Daily LifeTelecommunications(a) Optical fibres have many advantages compared to conventional cables in the transmission of information. Optical fibres are lightweight, flexible, electrically non-conducting (thus are not affected by electromagnetic interference) and can transmit much more information (information is transmitted almost at speed of light, 3 x 108 ms -1).

Applications of Reflection of waves in Daily LifeTelecommunications(b) Infrared waves from a remote control of electrical equipment (television or radio) are reflected by objects in the surroundings and received by the television set or radio.