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.

Types 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.

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm

Types 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

The graph shows how the displacement of one particle at a particular distance from the source varies with time.Graph of the equation

TtAtAy 2sinsin

y

0 tT 2T

A

Variation of displacement with distance

The graph shows the displacement of the vibrating particles at different distances from the source at a certain instant.Graph of the equation

xAkxAy 2sinsin

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

xTtAy

)(sinvxtAy or

Phase DifferenceThe phase difference between two waves is the fraction of a cycle (in radians) by which one wave would have to be advanced or retarded to be in phase with the other.

B is ¼ cycle behind A

B starts here

displacement

time0

A

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

mTc

2

c

mklc

pc

Ec

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://www.walter-fendt.de/ph14e/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/Applets.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 (e.g. Sound waves).

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 wave 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 SonarDepth 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

Superposition of waves

Principle of superpositionPulses and waves pass through each other

unaffected.The total displacement is the vector sum of the

individual displacements due to each wave.

http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave2.html

Interference

Constructive interferencePath difference =n

Destructive interferencePath difference = (n+½)

http://www.colorado.edu/physics/2000/schroedinger/index.html

BeatsBeats are formed when two waves with slightly different frequencies interfere with each other.

http://surendranath.tripod.com/Applets.html

http://www.school-for-champions.com/science/sound_beat.htm

Beat FrequenciesBeat frequency is the combination of two frequencies that are very close to each other. The sound will fluctuate in volume according to the difference in their frequencies. fb = | f1 − f2 | wherefb is the beat frequency f1 and f2 are the two sound frequencies | f1 − f2 | is the absolute value or

positive (+) value of the difference

Applications of BeatsTuning of Musical InstrumentsA piano tuner will strike a key and then compare

the note with a tuning fork. If the piano is slightly out of tune, he will be able to hear the beat frequency and then adjust the piano wire until it is at the same frequency as the tuning fork.

Police RADAR the beat frequency between the directed and

reflected waves provides a measure of the vehicle speed.

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.

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

Nodes Antinodes

Useful WebsitesReflection of waves

http://www.cdli.ca/courses/phys2204/unit04_org01_ilo07/b_activity.html http://phoenix.phys.clemson.edu/labs/224/microwaves/index.html#setup http://www.scienceinschool.org/2009/issue12/microwaves

Interference of microwaves (1)

Interference of microwaves (2)

ProcedureSet up the transmitter symmetrically behind the two gaps, each of which is a half-wavelength wide.Move the receiver in an arc, always the same distance from the gaps. The current through the meter should rise and fall to show about five maxima. Show that, when either gap is covered with a metal plate, the received signal decreases if the receiver is at a maximum but increases if the receiver is at a minimum.

Interference of microwaves (3)