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# Chapter 6-waves-2012

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### Chapter 6-waves-2012

1. 1. Hoo Sze Yen www.physicsrox.com Physics SPM 2012CHAPTER 6:WAVES6.1 Wave Basics• Waves are generated by oscillating/vibrating systems• An oscillation is the back-and-forth movement of an oscillating system through a fixed path6.1.1 Wave Fronts• Wave fronts are the lines or surfaces connecting the particles moving at the same phase and are at the same distance from a wave source.• Wave fronts are always perpendicular to the direction of propagation. Plane waves Circular wavesChapter 6: Waves Page 1 of 14
2. 2. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.1.2 Types of WavesTransverse Waves Longitudinal WavesTransverse waves are waves which oscillate Longitudinal waves are waves whichperpendicular to the direction of oscillate parallel to the direction ofpropagation. propagation.E.g: Light waves E.g: Sound waves6.1.3 Amplitude, Period and Frequency• Amplitude is the maximum displacement of an object from its equilibrium position [m]• Period is the time taken for a particle to make one complete oscillation [s] time taken Period, T = number of oscillatio ns• Frequency is the number of complete oscillations in one second [Hz] number of oscillations Frequency, f = time taken 1 f = TChapter 6: Waves Page 2 of 14
3. 3. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.1.4 GraphsDisplacement-time graph Amplitude AmplitudeDisplacement-distance graph6.1.5 Wave Equation v = fλwhere v = velocity of the wave [m s-1] f = frequency of the wave [Hz] λ = wavelength [m]6.1.6 Damping and Resonance• An oscillating system which has a reducing amplitude over time is said to be undergoing damping. Damping is due to lost energy through friction and heat. External damping: Loss of heat energy because of friction with the air Internal damping: Loss of heat energy because of the compression and tension of the molecules in the systemChapter 6: Waves Page 3 of 14
4. 4. Hoo Sze Yen www.physicsrox.com Physics SPM 2012• A system that is forced to oscillate continuously with provided external energy is said to be undergoing forced oscillation• Natural frequency is the frequency of a system that is left to oscillate freely without an external force• An object that is forced to oscillate at its natural frequency is said to be vibrating at resonance. An object vibrating at resonance has the maximum amplitude because it is receiving maximum energy from the external systemBarton’s Pendulum• When the control pendulum X is oscillated, its energy is transferred to the other pendulums through the string.• The other pendulums are forced to oscillate at the same frequency as pendulum X.• Because pendulum D has the same natural frequency as X (same length), pendulum D will oscillate at resonance and will have the maximum amplitude.6.1.7 Ripple tankAll water wave phenomena are observed through ripple tanks.Chapter 6: Waves Page 4 of 14
5. 5. Hoo Sze Yen www.physicsrox.com Physics SPM 2012 Formation of wave shadows on the screen6.2 Wave Reflection6.2.1 Reflection of Waves The angle of incidence = The angle of reflection6.2.2 Applications• Embankments to protect the ports, beaches, etcChapter 6: Waves Page 5 of 14
6. 6. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.3 Wave Refraction6.3.1 Water wave refraction• Water travels faster in deep waters and slower in shallow waters• Therefore, the wavelength of water waves in deep water is bigger than the wavelength in shallow water. λ1 > λ 2• When traveling from deep to shallow, the waves refract towards normal• When traveling from shallow to deep, the waves refract away from normal6.3.2 Water wave refraction patternsChapter 6: Waves Page 6 of 14
7. 7. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.3.3 Water wave refraction at the seaside• As the wind blows the sea towards the beach, the decreasing depth causes the speed of the water waves to slow down• The refraction effect causes the wave fronts to curve to be almost parallel to the beach• In the middle of the sea, the wave fronts are almost in a straight line, as per A1B1C1D1 due to the same water depths• As the waves approach the beachline, the wave fronts begin to curve to follow the shape of the beachline, as per A2B2C2D2 and A3B3C3D3• Energy from A1B1 is focused on the peninsula at A3B3 causing the peninsula to be hit by strong waves• Energy from B1C1 is spread out through the bay at B3C3 causing the water at the bay to be calmer6.3.4 Sound wave refraction Sound refraction in the daytime Sound refraction at nightIn the day, the air above the ground is hotter At night, the air above the ground is colderthan the air higher in the atmosphere. As than the air higher in the atmosphere. Assound travels from hot air to cold air, its sound travels from cold air to hot air, itsspeed decreases and refracts towards normal; speed increases until a point where the anglehence the sound wave curves upwards. of incidence is greater than the critical angle and total internal reflection occurs; hence the sound wave curves downeards.6.4 Wave Diffraction6.4.1 Wave diffraction• Diffraction is more visible when: The wavelength of the wave is bigger The obstacle is smaller than the wavelength The aperture is smaller than the wavelengthChapter 6: Waves Page 7 of 14
8. 8. Hoo Sze Yen www.physicsrox.com Physics SPM 2012 Smaller aperture Bigger aperture Diffraction is more obvious Diffraction is less obvious Smaller obstacle Bigger obstacle Diffraction is more obvious Diffraction is less obvious Round obstacle6.4.2 Applications of diffraction• Embankment to protect portsChapter 6: Waves Page 8 of 14
9. 9. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.5 Wave Interference6.5.1 Principle of superposition• The principle of superposition state that when two waves propagate through the same point at the same time, the displacement at that point is the vector sum of the displacement of each individual wave.• Two wave sources which are coherent have the same frequency and the same phase or phase difference.• The superposition effects creates interference Constructive interference Destructive interference6.5.2 Interference patternChapter 6: Waves Page 9 of 14
10. 10. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.5.3 Interference equation ax λ= Dwhere λ = wavelength [m] a = distance between sources [m] x = distance between two successive antinodal/nodal lines [m] D = distance between a and x [m]6.5.4 Different frequencies Low frequency High frequency (large wavelength) (small wavelength) Value of x is larger Value of x is smaller6.5.5 Different distance between the sources Larger distance between the sources Smaller distance between the sources Value of x is smaller Value of x is largerChapter 6: Waves Page 10 of 14
11. 11. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.6 Sound Waves• Sound waves are longitudinal waves.• Sound waves are mechanical waves; therefore they need a medium to propagate.• The medium undergoes compression and rarefaction to transfer the energy of the sound waves from one point to another.6.6.1 Speed of sound• Speed of sound is fastest in solids, followed by liquids, then gases.• Speed of sound increases with temperature6.6.2 Amplitude and Loudness• The loudness of sound is dependent on the amplitude of the wave.• The higher the amplitude, the louder the sound.6.6.3 Frequency and Pitch• The pitch of sound is dependent on the frequency of the wave.• The higher the frequency, the higher the pitch.6.6.4 Quality of Sound• Different musical instruments can produce notes of the same loudness and pitch, and yet they are easily discernible from one another.• This is because of the quality or timbre of the note produced by the individual musical instruments.• Quality of sound depends on the shape of the sound waves generated by the musical instruments.• Each note consists of a fundamental frequency that is mixed with weaker frequencies called overtones.6.6.5 Frequency rangesInfrasonic / Subsonic Frequency too low for human ears Below 20 HzAudio frequency Frequency audible to human ears 20 – 20 000 HzUltrasonic / Supersonic Frequency too high for human ears Above 20 000 Hz6.6.6 Noise• Sounds with frequencies which change randomly are known as noise• Exposure to noise for an extended period of time can create psychological and physical problemsChapter 6: Waves Page 11 of 14
12. 12. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.6.7 Application of sound wave phenomena• Echoes (Sound wave reflection) In an auditorium, concert hall or music studio, echoes must be taken into account to ensure good acoustics• Hyperbolic shape of sound waves Ampitheatres are usually designed in a hyperbole to enable better sound travel• Sonar Supersonic waves used to measure the ocean depths and to detect objects in the ocean The transmitter releases an ultrasonic pulse which echoes off the ocean bed or object and is detected by a hydrophone• Ultrasonic waves in medicine Diagnostics – to create a picture or an image of an internal organ. E.g. foetus in mother’s womb Ultrasonic drill – to cut a decaying part of the tooth• Ultrasonic waves in industries Ultrasonic echoes – to detect flaws in a metal structure. E.g. in railway tracks Ultrasonic drill – to cut holes in glass and steel High frequency vibration – to clean instruments and fragile items6.7 Electromagnetic Waves• Electromagnetic waves are electrical and magnetic fields oscillating perpendicular to each other around a single axis6.7.1 CharacteristicsElectromagnetic waves have the followingcharacteristics:• Transverse wave• Fulfills the wave equation v=fλ• Travels at the same speed (speed through vacuum: c = 3 × 108 m s-1)• Does not need a medium to propagate• Can be polarized Polaroid is a type of material which allows waves to penetrate through in one plane only PolarizationChapter 6: Waves Page 12 of 14
13. 13. Hoo Sze Yen www.physicsrox.com Physics SPM 20126.7.2 Electromagnetic Wave SpectrumElectromagnetic wave Source Characteristic Uses Gamma ray • Nuclear • High energy • Kill cancer cells reaction • High penetration • Sterilization (fission, • Extremely • Food preservation fusion) dangerous • Kill agricultural pests • Detect flaws or worn parts in car engines X-ray • X-ray tubes: • High energy • Detect bone flaws or high-velocity • High penetration fractures electrons • Extremely • Detect structural or hitting heavy dangerous machine flaws metal targets • Investigate crystal structures and elements in a material • Examine bags at the airport Ultraviolet • The sun • Absorbed by • Treats the skin with ray • Mercury glass and the the right exposure (forWAVELENGTH, λ (m) ← vapour lamps ozone layer Vitamin D) FREQUENCY, f (Hz) → • Extremely • Enables chemical • Detects counterfeit hot objects reactions, skin money burns, skin cancer Visible light • The sun • Consists of seven • Enables vision • Light bulbs colours with their • Enables photography • Fire own respective • Photosynthesis wavelengths and • Optic fibre to see frequencies inside tissues and organs • Laser light in optic fibre for communication Infrared ray • The sun • Heat ray • Physiotherapy • Heater • Enables a hot • Pictures of internal • Hot or feeling organs burning items • Satellite pictures Microwave • Klystroms • Penetrates the • Communication – atmosphere satellite, radar • Cooking Radiowave • Electrical VHF & UHF • UHF currents • Radio and television • VHF oscillating at SW, MW & LW • SW the • Radio broadcast • MW transmitting • LW aerialChapter 6: Waves Page 13 of 14
14. 14. Hoo Sze Yen Physics SPM 20106.8 Wave PhenomenaPhenomena Changing Water waves Sound waves Light waves characteristicsReflection Unchanged: • Speed • Frequency i r • Wavelength Change: • Amplitude Incident Reflected ray normal rayRefraction Unchanged: • Frequency Change: • Speed Carbon dioxide: Converges the • Wavelength sound waves (louder) • Amplitude Helium: Diverges the sound waves (softer)Diffraction Unchanged: Results using single-slit slide: • Speed • Frequency • Wavelength Change: Ray box Slide Screen • AmplitudeInterference Unchanged: • Speed • Frequency Results using Young double-slit: • Wavelength Change: • AmplitudeChapter 6: Waves Page 14 of 14