Types of Waves (1)Mechanical waves and electromagnetic waves

Some waves require a material substance called a medium through which to travel. Waves like this are called mechanical waves.

Examples: water waves, sound waves and seismic waves etc.

Electromagnetic waves require no medium through which to travel.

Example: radio waves, microwaves and light etc.

Type of Waves (2)

Transverse waves and longitudinal waves

In transverse wave, the direction in which the disturbances take place is at right angles to the direction of propagation of the waves.

In longitudinal wave, the disturbances take place in a direction parallel to the direction of propagation of the waves.

Type of Waves (3)

Progressive waves and stationary waves

A wave which transmits energy from the source to the space surrounding the source is called a progressive wave (travelling waves).

In certain conditions, waves energy is localized. When this happens, the waves are called stationary waves (standing waves).

Comparison of stationary waves and progressive waves

Over one wavelength all particles have different phases.

All the particles between two adjacent nodes are in phase.

The amplitude is the same for all particles along the wave.

The amplitude varies from zero at a node to maximum at an antinode.

Waveform moves through the medium, carrying energy, but not the medium, with it.

Waveform does not move, but has nodes at fixed places, energy is not carried away.

Travelling wavesStationary waves

Wave Equations

In a sinusoidal wave, each particle undergoes simple harmonic motion about its equilibrium position.This gives the equation

tAy sinwhere = 2 f

or kxAy sinwhere k = 2π/λ

Variation of Displacement with Time

Graph of the equation T

tAtAy

2sinsin

y

0 tT 2T

A

Variation of displacement with distance

Graph of the equation x

AkxAy2

sinsin

y

0 xλ 2λ

A

Wave Function for a Sinusoidal wave (1)

Mathematically the variable y depends on two variables x and t. So the combined equation is

)(2sin

x

T

tAy

)(sinv

xtAy or

Velocity of Propagation of Mechanical Waves (1)

It is usually found that the speed of a mechanical wave is affected by two factors. One of the factors is associated with the

strength of the elastic coupling between particles in the medium through which the waves travels.

The other factor is associated with the inertia of the moving particles.

Velocity of Propagation of Mechanical Waves (2)

Equations giving the speed of different types of wave

Transverse wave on string

Transverse ripples on a pond

Longitudinal wave on a spring

Longitudinal wave on a rod

Sound wave in a gas

m

Tc

2

c

m

klc

p

c

E

c

Huygens’ PrincipleEvery point on a wavefront can be considered as a source of tiny wavelets that spread out in the forward direction at a speed of the wave itself.

The new wavefronts is the envelop of all the wavelets – that is, the tangent to all of them.

http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens1.html

Huygens’ Principle and the Law of Reflection

The angle of incidence=the angle of reflection

A

B

A’

B’vt

vt

http://home.a-city.de/walter.fendt/phe/huygenspr.htm

Huygens’Principle and the Law of Refraction

Sin i/sin r = v1/v2 = 1/2

v1t

v2t

A

B

B’A’

Phase Change on Reflection (1)

Fixed end reflection

There is a phase Change of after reflection

http://surendranath.tripod.com/Twave/TwaveRefTran/TwaveRefTran.html

Phase Change on Reflection (2)A wave travelling from a less dense medium to a denser medium

Phase Change on Reflection (3)

Free end reflection

No phase changeoccurs

Phase Change on Reflection (4)A wave travelling from a denser medium to a less dense medium

Phase Change on Reflection (5)

Phase changes also occurs when longitudinal waves are reflected.

Fixed end Free end

C R

R C

R C

R C

Uses of Reflected WavesRadar (Radio Detection And Ranging) Pulses of high-frequency radio waves are

transmitted towards distant objects and their reflections are received between the transmitted pulse.

Sonar (Sound Navigation And Ranging) Pulses of ultrasonic waved are transmitted

towards under water objects, and their reflected pulses are detected.

Ionospheric Waves Radio waves from the transmitter travels through

air and is reflected by the ionosphere.http://www.pbs.org/wgbh/nova/lochness/sonar2.html

Uses of RadarDetect the presence of an object at a distance Detect the speed of an object Map something-to create detailed topographic maps of the surface of planets and moons.

http://www.howstuffworks.com/radar2.htm

Uses of Sonar

Depth soundersTo measure the

depth of the sea

Fish findersTo detect shoals

of fish

Side Scan sonarTo map the

ocean floorhttp://www.pbs.org/wgbh/nova/lochness/sonar.html

Atmospheric Windows to EM Radiation

Reflection of Radio Waves from the Ionosphere

Propagation of Radio Waves

Transverse wavesParticles vibrate along a line which is perpendicular to the direction of travel of the disturbance.

Longitudinal WavesParticles vibrate along a line which is parallel to the direction of travel of the disturbance.

Compression Rarefaction

Stationary WavesA stationary wave doesn’t appear to be travelling.

Nodes Antinodes