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chapter 6 - waves

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  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 1 of 14

    CHAPTER 6:

    WAVES

    6.1 Wave Basics

    Waves are generated by oscillating/vibrating systems An oscillation is the back-and-forth movement of an oscillating system through a fixed

    path

    6.1.1 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 waves

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 2 of 14

    6.1.2 Types of Waves

    Transverse Waves Longitudinal Waves

    Transverse waves are waves which oscillate perpendicular to the direction of propagation.

    Longitudinal waves are waves which oscillate parallel to the direction of propagation.

    E.g: Light waves E.g: Sound waves

    6.1.3 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]

    nsoscillatio ofnumber takentime

    Period, =T

    Frequency is the number of complete oscillations in one second [Hz]

    takentimensoscillatio ofnumber

    Frequency, =f

    Tf 1=

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 3 of 14

    6.1.4 Graphs

    Displacement-time graph

    Displacement-distance graph

    6.1.5 Wave Equation

    v = f

    where v = velocity of the wave [m s-1] f = frequency of the wave [Hz] = 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 system

    Amplitude

    Amplitude

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 4 of 14

    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 system

    Bartons 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 tank

    All water wave phenomena are observed through ripple tanks.

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 5 of 14

    Formation of wave shadows on the screen

    6.2 Wave Reflection

    6.2.1 Reflection of Waves

    The angle of incidence = The angle of reflection

    6.2.2 Applications

    Embankments to protect the ports, beaches, etc

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 6 of 14

    6.3 Wave Refraction

    6.3.1 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.

    1 > 2

    When traveling from deep to shallow, the waves refract towards normal When traveling from shallow to deep, the waves refract away from normal

    6.3.2 Water wave refraction patterns

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 7 of 14

    6.3.3 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 calmer

    6.3.4 Sound wave refraction

    Sound refraction in the daytime Sound refraction at night In the day, the air above the ground is hotter than the air higher in the atmosphere. As sound travels from hot air to cold air, its speed decreases and refracts towards normal; hence the sound wave curves upwards.

    At night, the air above the ground is colder than the air higher in the atmosphere. As sound travels from cold air to hot air, its speed increases until a point where the angle of incidence is greater than the critical angle and total internal reflection occurs; hence the sound wave curves downeards.

    6.4 Wave Diffraction

    6.4.1 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 wavelength

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 8 of 14

    Smaller aperture Diffraction is more obvious

    Bigger aperture Diffraction is less obvious

    Smaller obstacle Diffraction is more obvious

    Bigger obstacle Diffraction is less obvious

    Round obstacle

    6.4.2 Applications of diffraction

    Embankment to protect ports

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 9 of 14

    6.5 Wave Interference

    6.5.1 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 interference

    6.5.2 Interference pattern

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 10 of 14

    6.5.3 Interference equation

    Dax

    =

    where = 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 (large wavelength)

    High frequency (small wavelength)

    Value of x is larger Value of x is smaller

    6.5.5 Different distance between the sources

    Larger distance between the sources Smaller distance between the sources Value of x is smaller Value of x is larger

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 11 of 14

    6.6 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 temperature

    6.6.2 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 ranges

    Infrasonic / Subsonic Frequency too low for human ears Below 20 Hz Audio frequency Frequency audible to human ears 20 20 000 Hz Ultrasonic / Supersonic Frequency too high for human ears Above 20 000 Hz

    6.6.6 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 problems

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 12 of 14

    Polaroid is a type of material which allows waves to penetrate through in one plane only

    Polarization

    6.6.7 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 mothers 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 items

    6.7 Electromagnetic Waves

    Electromagnetic waves are electrical and magnetic fields oscillating perpendicular to each other around a single axis

    6.7.1 Characteristics

    Electromagnetic waves have the following characteristics: Transverse wave Fulfills the wave equation v=f Travels at the same speed (speed through vacuum: c = 3 108 m s-1) Does not need a medium to propagate Can be polarized

  • Hoo Sze Yen www.physicsrox.com Physics SPM 2012

    Chapter 6: Waves Page 13 of 14

    6.7.2 Electromagnetic Wave Spectrum

    Electromagnetic wave Source Characteristic Uses Gamma ray Nuclear

    reaction (fission, fusion)

    High energy High penetration Extremely

    dangerous

    Kill cancer cells Sterilization Food preservation Kill agricultural pests Detect flaws or worn

    parts in car engines X-ray X-ray tubes:

    high-velocity electrons hitting heavy metal targets

    High energy High penetration Extremely

    dangerous

    Detect bone flaws or fractures

    Detect structural or machine flaws

    Investigate crystal structures and elements in a material

    Examine bags at the airport

    Ultraviolet ray

    The sun Mercury

    vapour lamps Extremely

    hot objects

    Absorbed by glass and the ozone layer

    Enables chemical reactions, skin burns, skin cancer

    Treats the skin with the right exposure (for Vitamin D)

    Detects counterfeit money

    Visible light The sun Light bulbs Fire

    Consists of seven colours with their own respective wavelengths and frequencies

    Enables vision Enables photography Photosynthesis Optic fibre to see

    inside tissues and organs

    Laser light in optic fibre for communication

    Infrared ray The sun Heater Hot or

    burning items

    Heat ray Enables a hot

    feeling

    Physiotherapy Pictures of internal

    organs Satellite pictures

    Microwave Klystroms Penetrates the atmosphere

    Communication satellite, radar

    Cooking

    WA

    VEL

    ENG

    TH, (m

    )

    Radiowave UHF VHF SW MW LW

    FREQ

    UEN

    CY, f (H

    z)

    Electrical currents oscillating at the transmitting aerial

    VHF & UHF Radio and television SW, MW & LW Radio broadcast

  • Hoo Sze Yen Physics SPM 2010

    Chapter 6: Waves Page 14 of 14

    6.8 Wave Phenomena

    Phenomena Changing characteristics

    Water waves Sound waves Light waves

    Reflection

    Unchanged: Speed Frequency Wavelength

    Change: Amplitude

    Refraction Unchanged: Frequency

    Change: Speed Wavelength Amplitude

    Carbon dioxide: Converges the sound waves (louder) Helium: Diverges the sound waves (softer)

    Diffraction Unchanged: Speed Frequency Wavelength

    Change: Amplitude

    Results using single-slit slide:

    Interference Unchanged: Speed Frequency Wavelength

    Change: Amplitude

    Results using Young double-slit:

    i r

    normal Incident ray

    Reflected ray

    Ray box Slide Screen