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BTEC APPLIED SCIENCE UNIT 1 PHYSICS NOTES

WAVES

BTEC UNIT 1 PHYSICS NOTES Holy Cross College BTEC Applied Science Department

CONTENTS:

C1 WORKING WITH WAVES

1. WAVES AND OSILLATIONS2. THE WAVE EQUATION3. OVERLAPPING WAVES4. DIFFRACTION GRATINGS5. STATIONARY WAVES6. MUSICAL INSTRUMENTS7. SPEED, TENSION AND MASS PER UNIT LENGTH

C2 WAVES IN COMMUNICATION

1. REFRACTIVE INDEX2. TOTAL INTERNAL REFLECTION3. OPTICAL FIBRES

C3 ELECTROMAGNETIC WAVES

1. REGIONS OF THE ELECTROMAGNETIC SPECTRUM2. INTENSITY OF WAVES AND THE INVERSE SQAURE LAW

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C1 WORKING WITH WAVES

1. WAVES AND OSCILLATIONS

DESCRIBING OSCILLATIONS

When an object such as a simple pendulum oscillates its graph of displacement against position goes through a repeating cycle.

Key Terms :

The DISPLACEMENT of a vibrating particle is its distance and direction from its equilibrium position. The AMPLITUDE, a, is the maximum displacement of the oscillating object (from its centre point).

For a transverse wave, this is the height of a wave crest or the depth of a wave trough from its equilibrium position.

The WAVELENGTH of a wave is the least distance between two adjacent vibrating particles with the same displacement and velocity at the same time (e.g. the distance between two adjacent crests or troughs)

The PERIOD, T, is the time for one complete oscillation (measured in SECONDS, s)

The FREQUENCY, f, is the number of complete oscillations per second (measured in Hertz, Hz)

f = 1T ; T=1

f

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3. THE WAVE EQUATION: When one particle in a medium oscillates it sets the particles next to it oscillating and this produces a

wave, which moves through the medium.

A wave allows energy to be transferred from one point to another some distance away without any particles of the medium travelling between the two points.

e.g. sound waves transfer energy from the source to the ear without any transfer of the medium.

If the source or origin of the waves oscillates with a FREQUENCY, f, then each point in the medium

oscillates with the same frequency. The source repeats its motion f times per second so a repeating wave form is observed spreading out from the source.

The distance between points at the same stage in their oscillation on successive wave forms (such as

two crests) is called the WAVELENGTH, λ.

Hence the WAVESPEED or WAVE VELOCITY, v (the distance moved by the wave form per second) is given by:

v = f λ

This WAVE EQUATION is true for all wave motion.

TYPES OF WAVE

Waves can be divided into two types based on the relative directions of the wave motion and the direction of particle oscillations:

TRANSVERSE WAVES where the vibrations of the medium are perpendicular to the direction of wave travel or propagation.

e.g. water waves, waves on a string, electromagnetic waves.

LONGITUDINAL WAVES where the vibrations of the medium are in the same direction as the direction of wave travel or propagation.

e.g. sound waves in air.Longitudinal waves are propagated by compressions and rarefactions moving through the medium (regions of high and low density).

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TRANSVERSE WAVES:

Transverse waves are waves in which the oscillations are PERPENDICULAR to the direction of propagation (direction of energy transfer). The movement of a transverse wave is illustrated in the diagrams below.

Each particle vibrates with the same amplitude and frequency, and the wave is shown successively at t = 0, T/4, T/2, and 3T/4, where T is the period.

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LONGITUDINAL WAVES:

In contrast to a transverse wave, a longitudinal wave is one in which the oscillations occur in the parallel to the direction of travel of propagation of the wave. The diagram illustrates the movement of a longitudinal wave. The lines show the actual positions of the particles whereas the graph shows the displacement of the particles from their equilibrium positions.

Some points to note:

The displacements of the particles produce regions of high density (compressions) and low density (rarefactions) along the wave.

These regions move along with the speed of the wave.

Each particle vibrates about its mean position with the same amplitude and frequency.

At the compressions and rarefactions, the displacement of the particles is zero. Therefore, the regions of greatest compression are one quarter wavelength (¼ of a cycle) ahead of the greatest displacement in the direction of the wave.

At the compressions the pressure is higher than normal, at the rarefactions the pressure is lower than normal. These positions of maximum and minimum pressure are ¼ of a cycle out of phase with the positions of maximum and minimum displacement.

The wavelength is equal to the distance between successive compressions.

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SOUND WAVES

Sound waves consist of longitudinal vibrations of the molecules of the medium through which the sound travels.

Sounds may differ from each other in three ways:

(1) PITCH (2) LOUDNESS (3) QUALITY

PITCH is analogous to colour for light waves and depends on the frequency of the sound wave. The range of audible frequencies is from approximately 20 - 20 000 Hz. The relative pitch or frequency of notes is important in music. If the frequency of a note doubles its pitch is said to increase by one octave.

LOUDNESS is a measure of the intensity of a sound wave. The intensity of a wave is proportional to the amplitude of vibration squared.

When the same note is played on two different instruments the note can be distinguished. This is because the notes are not "single" frequencies. They consist of the main or fundamental frequency and several overtones (which are multiples of the fundamental). The number and amplitude of these overtones varies

from one instrument to another and determines the QUALITY of the note (more on this when we look at standing waves)

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3. OVERLAPPING WAVESPHASE:

If two objects oscillate with the same frequency and are at the same stage in their oscillations at the same time they are in phase.

If two objects oscillating with the same frequency are not in phase then the phase difference measures how much out of step they are.

Phase difference can be expressed as a fraction of a cycle, or as an angle. One complete cycle is equivalent to 360º, a shift equivalent to one wavelength in distance or one period in time.

If two objects are 180º out of phase, they are said to be in anti-phase. PROGRESSIVE WAVES:

Both the transverse and longitudinal waves described previously are progressive waves. This means that their wave profile moves (or progresses) through the medium with the speed of the wave motion. If a graph of displacement against position is drawn the wave profile is repeated, and the distance between two points at the same stage in their vibration is called the wavelength. If one point is chosen and a graph of displacement against time is drawn for that point the graph repeats itself at equal time intervals. The

repeat time is called the periodic time, T, for the wave.

In a progressive wave the amplitude of vibration is the same at all points provided there is no loss in energy but successive points are at a different stage in their vibration. We say the phase of the vibrations

varies with position. Two points separated by a distance λ, the wavelength, are vibrating in phase (they are one complete cycle out of phase).

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SUPERPOSITIONWhen two waves travel through a medium their combined effect at any point can be found using the principle of superposition.

This states that the resultant displacement at any point is the sum of the separate displacements due to the individual waves.

The diagrams below illustrate the principle of superposition:

If two waves of the same frequency and amplitude which are in phase add together they reinforce each other – this is constructive interference.

If two waves of the same frequency and amplitude which are half a cycle out of phase add together they cancel each other – this is destructive interference.

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CONSTRUCTIVE INTERFERENCE

DESTRUCTIVE INTERFERENCE


INTERFERENCEWhen two (or more) sets of waves overlap they can give interference effects. This occurs when:

The two sets of waves must be COHERENT (have the same frequency and a constant phase relationship).

Where the two waves combine in phase they add constructively. Where the two waves combine in anti-phase they add destructively. This phase difference occurs because the waves have travelled different distances from their

sources.

We can think of the different distances that the waves travel from their sources to a point relative to the wavelength of the wave:

The PATH LENGTH is the distance travelled by a wave from the source to a point, measured in metres.

The PATH DIFFERENCE is the difference in path lengths for the two waves.

- Where the path difference is an integer number of wavelengths (λ, 2λ, 3λ, 4λ ... etc. metres), the waves meet in phase and constructive interference occurs.

- Where the path difference is half a wavelength, one and a half wavelengths (0.5λ, 1.5λ, 2.5λ, 3.5λ ... etc. metres) etc., the waves meet in anti-phase and destructive interference occurs.

Interference patterns in a ripple tank Interference patterns produced(view looking down on wave) with white light (view projected onto a screen)

The diagrams above show interference patterns produced using a ripple tank and white light.

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The schematic diagram below shows how wavefronts emanating from two sources meet in phase (e.g. crest meets crest, trough meets trough) and in anti-phase (e.g. crest meets trough), forming fringes of constructive and destructive interference.

YOUNG’S DOUBLE SLIT EXPERIMENT

Interference can be produced with visible light provided the spacing between the two sources of waves is small. This spacing must be similar in size to the wavelength of the light. As visible light has a wavelength between 400 nm to 750 nm this is relatively uncommon.

The diagram below shows how this can be demonstrated using visible light. A laser gives a coherent light source, this illuminates two narrow slits about 0.1 mm apart. The light is diffracted (spread out) by the two slits and overlaps. An interference pattern can be observed on a screen 2 to 5 m from the slits.

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The spacing of the positions of constructive and destructive interference depends on the spacing of the slits and the wavelength of the light:

If the slits are closer together the interference positions are further apart. If the wavelength increases the spacing increases.

The Young’s Double Slit Experiment provides evidence that light behaves as a wave.

INTERFERENCE PATTERNS IN ACTION

THIN FILMS AND IRIDESCENCEInterference produces the colours seen in thin films such as a soap film, or in nature when creatures display IRIDESCENCE.

When light hits the surface of the bubble or thin film, some is reflected back off the film, whilst

some is transmitted through the film. When the transmitted light hits the boundary on the other side of the film, some is again reflected.

Both reflected beams of light are coherent. The two reflected beams of light then meet up and superpose. If the thickness of the soap film is t then the light reflected from the

back travels an extra distance of 2 × t.

If 2t is a whole number of wavelengths the two lots of light will be in phase giving constructive interference.

If 2t is ½λ, or 1½λ or 2½λ etc. the two sets of waves will be half a cycle out of phase (in antiphase), giving destructive interference.

In white light there is the full range of colours, so the thin film may give constructive interference for one

colour if 2t (2 × thickness) matches the wavelength for that colour. The range of colours can be seen due to variations in the thickness of the film (and therefore of the wavelength of light undergoing constructive superposition), and because different angles for the light travelling through the film give different path differences (and therefore wavelengths of light which recombine with constructive superposition).

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t


CDs, DVDs AND BLU-RAYS

Data is recorded on CDs, DVDs and Blu-rays as a series of small bumps and pits within the grooves on the CD. A laser light is shone on to the surface of the CD and the reflected light is detected by a photodiode (which the light signal is converted into an electrical signal).

The height between the bumps and pits is equal to one quarter of the wavelength of the light beam (usually about 200 nm in CDs, which use red-light, and less for Blu-Rays).

When the light reflects from the edge of a bump, the reflected light from the top of the bump and the bottom of the adjacent pit have a path difference of half a wavelength. This results in DESTRUCTIVE interference, and no signal.

When the light reflects from the centre of a bump or pit, the reflected beams of light have no path difference, giving CONSTRUCTIVE interference.

The reflected laser light will then be on or off giving the 1s and 0s of the signal.

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4. DIFFRACTION GRATINGS

Diffraction is the spreading of waves when they go through a gap or past an edge.

Diffraction is evidence for the wave nature of light. Both light waves and water waves in a ripple tank show diffraction.

DIFFRACTION AROUND BARRIERSDiffraction is the name given to the "spreading" of waves when they pass around an obstacle or through an aperture (a gap between two obstacles). Diffraction occurs for all types of waves, but can demonstrated

using water waves in a ripple tank.

The pattern produced depends on the size of the obstacle or aperture, compared to the wavelength, λ:

- The narrower the gap the more the waves spread out

- The longer the wavelength the more the waves spread out.

Study the diagrams above and note that in the first and third diagrams the gap is the same size but more diffraction is observed in the one with the bigger wavelength. When drawing them do not change the wavelength!

If the gap is too small, very little wave energy gets through so the pattern is very faint.

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WAVEFRONTS

If all the wave energy travels in one direction then the wavefronts will be straight lines.

When we look at ripples in water we can usually see WAVEFRONTS.

The gap between each line of wavefronts is equal to the wavelength of the wave. Wavefronts from point sources are circular in shape like the ripples seen when a stone is dropped into water.

A Ripple tank:

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BTEC UNIT 1 PHYSICS NOTES Holy Cross College BTEC Applied Science Department A ripple tank is used to show wave effects such as diffraction and refraction.

SINGLE SLIT DIFFRACTION.

When light is passed through a narrow single slit diffraction is observed. However if you look carefully at the image on a screen or at the gap between two pencils held close together you will observe a bright central region and dark fringes either side. This is because of interference effects similar to those observed with two slits.

THE DIFFRACTION GRATING.A diffraction grating is simply a glass plate with many closely spaced parallel lines on it. In effect producing many small slits.

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Light passing through this diffraction grating is transmitted only at certain angles. The central one is called the zero order and the next the first order, second order etc. The zero order beam passes straight through. Destructive interference cancels out the light in the places in-between each order.

The angle between each order diffraction increases if:

Light of longer wavelength is used.A grating with slits closer together is used. (more lines per cm.)

When white light is shone through a diffraction grating, different frequencies of light (colours) are diffracted at different angles. This has the effect of dispersing light into spectra similar to using a prism. Blue light is diffracted less than red. See figure 4.

A typical diffraction image. Note the central fringe is twice as wide, and brighter than the others.

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Note in the diagram below of two slit interference we still see the diffraction pattern above caused by diffraction at the slits, but within it we also see the interference pattern from the superposition of waves.

Note that when a shorter wavelength of light is used (or higher frequency) e.g. green light rather than red, the diffraction angles are less.Position of diffraction pattern using different coloured light:

You can use the pattern of lines in an emission spectrum as a ‘fingerprint’ to identify which atoms and molecules are present in a particular chemical sample. First you record the spectra from pure samples of each gas. Then you use those results as a reference to identify the frequencies of spectral lines obtained from a sample of unknown composition.

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5. STATIONARY WAVES

Stationary waves are produced when two waves of similar amplitude and the same frequency travel in opposite directions through a medium and superpose. To produce a stationary wave the two waves must be coherent. This means they have the same frequency and either are in phase or have a fixed phase difference. If two waves of different frequency overlap then there will be no fixed pattern produced. In a stationary wave the wave profile does not move through the medium, it remains stationary.

Stationary waves can be set up whenever a wave is confined, e.g. a wave on a stretched string. The string is plucked and the wave travels along the string and is reflected at the fixed end. The wave and its reflection then overlap and add.

- Where the two waves are half a cycle out of phase they add destructively and the displacement is permanently zero. These points are called NODES (NO Displacement).

- At points where the two waves are in phase, they add constructively giving maximum amplitude. These points are called ANTINODES.

When one point between two nodes is at its maximum displacement, then all points between the two nodes are at their maximum displacement.

When a point between two nodes has zero displacement all points between the two nodes have zero displacement.

Each point between two nodes has a different amplitude of vibration from its neighbouring points. The points with maximum amplitude are called antinodes.

The wavelength λ of the wave is twice the distance between successive nodes (or antinodes). The

distance between successive nodes is half the wavelength, λ2 .

Whilst progressive wave transmit energy through a medium, this is not the case in a stationary wave: these can be used to store energy.

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The diagram below illustrates the vibration of a stationary wave on a stretched string.

Here: W X, Y and Z are at nodes, P, Q and R are at antinodes.

6. MUSICAL INSTRUMENTS

STRINGED INSTRUMENTSIn stringed instruments the string is made to vibrate. The wave produced travels to the fixed end and is reflected. The reflected wave and the original wave add to produce a standing wave on the string. As the string is fixed at both ends there must be a node at each end. The simplest mode of vibration consists of a single antinode between the two ends. This is called the first harmonic.

The wavelength, λ1, for the first harmonic of vibration can

be related to the length of the string, l by the equation:

λ1 = 2 l

The first harmonic of vibration of the string is inversely proportional to the length increases as the tension increases increases as the mass per unit length (thickness) of the string decreases

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Second harmonic) f =2 f1 ; = l

Third Harmonicf =3 f1 ; = 2

3 l

lf = f1 ; = 2 l

N N

N N N

N N N N

A

A A

AA

First harmonic, f1

A


The fundamental frequency f1 is given by: f 1=12l √ T

μwhere T is the tension in the string and µ is the mass per unit length)

The string can also vibrate in a series of more complicated modes: second, third, fourth etc. harmonics (see above). The frequency of a harmonic is a multiple of the first harmonic. The presence of these harmonics gives the sound from the instrument its particular quality.

COLUMNS OF AIRSounds can also be produced in closed (e.g. a pipe organ) and open (e.g. a flute) columns of air.

CLOSED PIPE INSTRUMENTSIn a pipe closed at one end there must be a displacement node at the closed end and a displacement antinode at the open end. The pressure nodes and antinodes will be ¼ of a wavelength out of step, with a node (normal pressure) at the open end and an antinode at the closed end. The first three modes of vibration for a closed pipe are shown below.

In pipe systems, the wavespeed, v, is equal to the speed of sound in air. The length of the pipe affects the wavelength and therefore frequency of the sound wave: the frequency is inversely proportional to the length of the air column.

In the first harmonic l = λ4 ; λ = 4l ; the fundamental frequency is thus f1 = v

λ= v

4 l The second harmonic has a wavelength 1/3 of the fundamental, so the frequency is 3f1. The third harmonic has a wavelength 1/5 of the first harmonic, so the frequency is 5f1.

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Third harmonic

f =5 f1 ; = 4

5¿¿ l

Second harmonic

f = 3 f1 ; = 4

3¿¿ l

First harmonicf = f1 ; = 4 l

AN N N N N NA A A A Al


OPEN PIPE INSTRUMENTSIn an open pipe there will be an antinode at each end of the pipe. This gives the patterns of vibration shown below.

The frequency is again inversely proportional to the length.

In the first harmonic l = λ2 so λ = 2 l ; the frequency of the first harmonic is f0 =

vλ= v

2l The second harmonic has a wavelength ½ of the first and therefore a frequency 2f1. The third harmonic has a wavelength 1/3 of the first and therefore a frequency 3f1.

The sound produced by a musical instrument depends on which overtones are present and how large an amplitude they have. If a guitar string is plucked in the middle then there will be little of the first overtone produced because this has a node in the middle of the wire. If a wind instrument is blown harder then more energy is given to the higher frequencies produced.

7. SPEED, TENSION AND MASS PER UNIT LENGTH

On a stretched string or rope, the wave speed is also related to the mass per unit length of the string and the tension in the string – over the same distance:

A heavy rope compared to a light slinky.

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Third harmonic)

f = 3 f1 ; = 2

3¿¿ l

Second harmonicf = 2 f1 ; = l

First harmonicf = f1 ; = 2 l

lA N A A A A A A A AN N N N N


A tight string compared with a loose string.

In fact, the wave speed can also be expressed as follows:

Where:

v = the wave velocity or speed (in ms-1)

T = the tension in the string (in Newtons it is a force)

µ = the mass per unit length (in kg/metre)

The formula given above tells us that the "tighter" the string (that is, the greater the tension placed on the string) the faster the waves will travel down its length. It also tells us that the "lighter" the string, that is,

the smaller its mass/length ratio, the faster the waves will travel down its length.

When playing a guitar, the note produced depends upon the frequency at which the string vibrates - and this depends on:

The tension in the string

The length of the string

The 'weight' (mass per metre) of the string - called in science the 'mass per unit length'.

Remember - wave speed is fixed by tension and mass per unit length.

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Direction of wave propagation

AIR GLASS

wavefronts


C2 WAVES IN COMMUNICATION

1. REFRACTIVE INDEXWhen a ray of light passes through a boundary between two media, the ray can either be TRANSMITTED (pass through the boundary between the two media) or REFLECTED (bounce back off the boundary).

Usually some of the light is reflected (obeying the laws of reflection), whilst the rest of the light is REFRACTED.

When light is transmitted across the boundary from a less optically dense to a more optically dense medium (e.g. from air to water or air to glass):

The wavespeed decreases. The wavelength decreases. The frequency remains constant.

Refraction is the change in the direction of propagation of the wave across the boundary. When waves hit a boundary at an angle, the change in wavespeed (and wavelength) either side of the boundary cause the wave to bend or REFRACT. The amount of refraction that occurs depends on the speed of the waves in each substance.

The refractive index, n, of a substance is given by the formula:

the refractiveindex of a substance , n=c /v

where c is the speed of light in a vacuum; v is the speed of light in the substance.

The refractive index of air is approximately 1.

The frequency remains unchanged whatever medium the light is travelling in.

Refraction occurs because the speed of light waves is different in each substance.

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incident ray

refracted ray

angle of incidence, i

angle of refraction, r


When light is travelling from one substance to another it can be shown that the refractive indices and angles of incidence/refraction are linked by the equation, called Snell’s law:

2. TOTAL INTERNAL REFLECTION AND THE CRITICAL ANGLE

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n=sin i /sin r


When a ray of light passes from a dense to a less dense medium (e.g. from glass to air) most of the light is transmitted or refracted and a weak beam is reflected (see diagram).

As the angle of incidence increases the angle of refraction increases. Eventually, as the angle of incidence

increases to the CRITICAL ANGLE, C, the angle of refraction reaches 90°. At the critical angle, the refracted ray travels along the boundary between the media, whilst the reflected ray is still weak.

If the angle of incidence is increased further, so it is greater than the critical angle), all the light is reflected. This is called TOTAL INTERNAL REFLECTION. There is no refracted ray.

It is important to remember that total internal reflection only occurs when light travels from a dense to a less dense medium.

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glass glass glass

airairair

i

r

ii

weak reflection

i = critical angle C i > critical angle, C

total internal reflection occurs

i < critical angle, C


3. OPTICAL FIBRES

Total internal reflection (TIR) is used to transmit light along optical fibres e.g. in endoscopes to see the inside of the body and in communications. As long as the curvature of the fibre is not too high the light undergoes TIR at the core-cladding boundary. In communications PULSES of light are transmitted.

Features of an optical fibre:

Feature Why?

Highly transparent coreMinimise absorption of light so amplitude of pulses does not

decrease (much)Cladding (lower refractive than

core)Reduce light loss from the core, prevent signals passing into other

fibres if the fibres touch – keep signals secureCladding (lower refractive than

core)Reduces pulse broadening

Very narrow core

Prevent modal (multipath) dispersionData transferred quicker

Less refraction out of core (angle of incidence less likely to fall below critical angle)

Sheath around cladding Protect the fibre from scratches

Modal dispersionThis occurs because light travelling down the axis of the fibre travels a different distance than light that repeatedly undergoes TIR. Light travelling at different angles arrives at the other end at different times. A pulse sent down a wide core would therefore become longer—PULSE BROADENING. If the pulse became too long it would merge with the next pulse. [Using cladding with a lower, but similar, refractive index to the core can also reduce pulse broadening as it reduces the critical angle. This means that those rays with

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very small angles of incidence (those that would take the longest paths down the fibre) do not undergo TIR and so these longer paths are eliminated.]

Material dispersionThis is another type of dispersion that occurs if white light is used instead of monochromatic light (light of a single wavelength). Because violet light travels slower in glass than red light, this would cause a pulse of white light to become broadened. Monochromatic light (or monochromatic infrared radiation) must be used in communications optical fibres.

Medical endoscopesA medical endoscope consists of two bundles of fibres. Light is sent down one bundle and used to illuminate the body cavity being viewed. This bundle incoherent—the positions of the fibres at each end does not matter. The second bundle has a lens over the end that forms an image of the body cavity. The light that formed this image travels along the fibres to the other end where it can be observed. This bundle needs to be coherent—the fibres at each end are at the same relative positions.

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C3 ELECTROMAGNETIC WAVES IN COMMUNICATION

1. ELECTROMAGNETIC WAVE SPECTRUM

Electromagnetic waves, including visible light, are transverse waves. They consist of oscillating electric fields (and magnetic fields). The electric and magnetic fields oscillate at 90º to the direction of propagation and at 90º to each other.

The electromagnetic spectrum is split into different regions, depending on the frequency and wavelength of the waves:

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There is a massive variation in wavelength (and frequency) from gamma rays (wavelength about 1 × 10 -

13m) to radio waves (wavelength up to 1000m).

In a vacuum, all electromagnetic waves travel at the speed of light, c = 3.0 x 108 ms-1).

Uses of waves on the Electromagnetic Spectrum

The Electromagnetic Spectrum Wavelength / frequency Used forRadio waves High wavelength / Low

frequencyRadio and TV transmission

Mobile phone communicationPlasma heating in fusion reactors

Industrial ovens

Microwaves Household ovensRADAR

Satellite and terrestrial communications

Infrared Night vision camerasOptical fibre communicationsSecurity movement detectors

Remote controlsSpectroscopy

Visible light LightingImaging – electric pictures

SignallingPhotosynthesis in plants

Spectroscopy

UV rays Insects use for visionGetting a suntan

Photosynthesis in plantsSpectroscopy

X rays Medical images – broken bones

Gamma rays Low wavelength / High frequency

Radiation sterilisation of equipmentMedial tracers

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BTEC UNIT 1 PHYSICS NOTES Holy Cross College BTEC Applied Science DepartmentApplications of EM SpectrumSatellite communications:

Use high power signals over very long distances Concentrated by a satellite dish Frequency band is 10-12 GHz??? The microwave range of the EM spectrum Satellite transponders receive incoming signals, amplify them and retransmit them as a download

signal on a different frequency band. This avoids interference.Mobile phone communications:

High power signals in a network Range is several km Frequency band is 800 MHz to 2.6 GHz Between UHF radio to microwave range Different bands are allocated to different operators e.g. O2 and Vodafone 2G, 3G and 4G cellular networks offer increasing speeds for data. Higher frequencies have greater data capacity but travel less distance through air and penetrate

into buildings less well.Bluetooth communications:

Low power device to device links Range only up to about 10 m Frequency band is 2.4 to 2.4835 GHz Called the “Industrial, Scientific, Medical (ISM) unlicensed Band” In between UHF radio and microwave frequencies Early Bluetooth devices interfered with Wi-Fi devices because both would use the same channel for

an extended period of time. Modern Bluetooth uses frequency-hopping – i.e. broadcasting in short bursts on a number of

different frequency channels across the band. This reduces the amount of data lost, and in most cases both Bluetooth and Wi-Fi can maintain

service.Wi-Fi communications:

Medium power signals in a networked system Frequency band is around 10 to 100 m See Bluetooth for Band name and early issues now resolved.

Infra-red communications: Low power device to device links Range is only a few metres Infra-Red wavelength 870 nm or 930 to 950 nm Frequency band is about 320 THz Used for remote controls and for data transfer between computers, phones etc. The longer wavelength band (930—950 nm) is better because it does not suffer from ‘sunlight

blinding’. This is where moisture in the atmosphere blocks the waves in sunlight (in the day only).

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2. INTENSITY OF WAVES AND THE INVERSE SQUARE LAW

The intensity of all electromagnetic radiation, including X-rays, obeys the inverse square law. This scientific law states that the further the point source of radiation is from the point at which you are measuring it, the lower the dose. If the distance is doubled, the intensity is reduced by four times (two squared). If the intensity is trebled, the intensity is reduced by nine times (three squared).

Suppose we have a point source of light as above. It will spread its energy equally in all directions. Therefore, if you wanted to find all of the points in space where the energy was of the same intensity you would have to draw a sphere around the source point. The bigger the radius of the sphere the greater the 'surface' over which the energy was spread.

The relationship between radius and sphere surface area is an inverse square relationship. That means that

intensity will depend on 1/r2. If you double the distance from the source the intensity will not halve but drop to a quarter of its value, tripling the distance will make the intensity drop to a ninth and so on.Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere surface at that radius.

Being strictly geometric in its origin, the inverse square law applies to many different phenomena.Point sources of gravitational force, electric field, light, sound or electromagnetic or nuclear radiation obey the inverse square law.

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http://www.cyberphysics.co.uk/general_pages/inverse_square/inverse_square.htm#radiation

http://www.cyberphysics.co.uk/general_pages/inverse_square/inverse_square.htm#electric

http://www.cyberphysics.co.uk/general_pages/inverse_square/inverse_square.htm#gravity

http://www.bbc.co.uk/schools/gcsebitesize/science/triple_edexcel/xrays_ecgs/xrays/revision/2/

BTEC UNIT 1 PHYSICS NOTES Holy Cross College BTEC Applied Science DepartmentThe Inverse Square Law can be used to compare wave intensities at different distances:

I = k/r2

I is the intensity of the wave in watts per m2

k is a constant

r is the distance from the source of the wave in metres.

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