[phy] chapter 6 waves 2012

Hoo Sze Yen www.physicsrox.com Physics SPM 2012

Chapter 6: Waves 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



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]

takentime

nsoscillatio ofnumber Frequency, =f

Tf

1=



6.1.4 Graphs Displacement-time graph

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

Amplitude

Amplitude



• 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.



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



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 > λ2

• 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



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



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



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



6.5.3 Interference equation

D

ax=λ

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 (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



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



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 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



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

VE

LE

NG

TH

, λ (

m) ←

Radiowave • UHF • VHF • SW • MW • LW

FR

EQ

UE

NC

Y, f

(Hz)

→

• Electrical currents oscillating at the transmitting aerial

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

Hoo Sze Yen Physics SPM 2010


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

[phy] chapter 6 waves 2012

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