The document provides an overview of key concepts in wave phenomena. It defines waves as oscillations generated by vibrating systems. Wave fronts connect particles moving in the same phase and are perpendicular to the direction of propagation. Transverse waves oscillate perpendicular to propagation, while longitudinal waves oscillate parallel. Amplitude is the maximum displacement from equilibrium, period is time for one oscillation, and frequency is oscillations per second. Waves can be described graphically and using the wave equation relating velocity, frequency, and wavelength. Reflection, refraction, diffraction, and interference are described for water and sound waves, as well as electromagnetic waves.

1. Hoo Sze Yen www.physicsrox.com Physics SPM 2012
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
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6.1.2 Types of Waves
Transverse Waves Longitudinal Waves
Transverse waves are waves which oscillate Longitudinal waves are waves which
perpendicular to the direction of oscillate parallel to the direction of
propagation. 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]
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 =
T
Chapter 6: Waves Page 2 of 14

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6.1.4 Graphs
Displacement-time graph
Amplitude
Amplitude
Displacement-distance graph
6.1.5 Wave Equation
v = fλ
where 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 system
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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 system
Barton’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 tank
All water wave phenomena are observed through ripple tanks.
Chapter 6: Waves Page 4 of 14

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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
Chapter 6: Waves Page 5 of 14

6. Hoo Sze Yen www.physicsrox.com Physics SPM 2012
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.
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 normal
6.3.2 Water wave refraction patterns
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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 At night, the air above the ground is colder
than the air higher in the atmosphere. As than the air higher in the atmosphere. As
sound travels from hot air to cold air, its sound travels from cold air to hot air, its
speed decreases and refracts towards normal; speed increases until a point where the angle
hence 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 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
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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 obstacle
6.4.2 Applications of diffraction
• Embankment to protect ports
Chapter 6: Waves Page 8 of 14

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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
Chapter 6: Waves Page 9 of 14

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6.5.3 Interference equation
ax
λ=
D
where 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 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
Chapter 6: Waves Page 10 of 14

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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
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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 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 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=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
Polarization
Chapter 6: Waves Page 12 of 14

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6.7.2 Electromagnetic Wave Spectrum
Electromagnetic 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 (for
WAVELENGTH, 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 aerial
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14. Hoo Sze Yen Physics SPM 2010
6.8 Wave Phenomena
Phenomena Changing Water waves Sound waves Light waves
characteristics
Reflection Unchanged:
• Speed
• Frequency
i r
• Wavelength
Change:
• Amplitude Incident Reflected
ray normal ray
Refraction 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
• Amplitude
Interference Unchanged:
• Speed
• Frequency Results using Young double-slit:
• Wavelength
Change:
• Amplitude
Chapter 6: Waves Page 14 of 14