wave phenomena r r d i

8/3/2019 Wave Phenomena r r d i

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WAVE PHENOMENA

REFLECTION, REFRACTION AND DIFFRACTION:

Waves can:

y be reflected;y refractedy be diffractedy interfereThese properties are shown by longitudinal and transverse waves and by mechanical and electromagnetic

waves.

REFLECTION

LIGHT

SPECULAR/REGULAR AND DIFFUSE REFLECTION OF LIGHT

Most things can onlybe seen when light bounces off the surface of the object and reaches our eyes. We call

this bouncing of light reflection. An object which reflects no light appears a dull black colour and is difficult

to see. An object which reflects all light appears the same colour as the light it is reflecting, so when white

sunlight shines on it, its colour is white.

A white sheet of paper and a highly polished silvery metal surface as on a mirrorboth reflect all the light that

falls on them; why then do they appear so different?

The difference is due to the nature of the surfaces of the materials.

y The surface of a polished sheet of metal or a mirror is very smooth and reflects all the parallel rays oflight from a particular source in one direction only; this called regular orspecular reflection.

y The irregular scattering of the light rays in different directions by a rough surface such as a sheet of paperis called diffuse reflection.


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REFLECTION IN A PLANE MIRROR

Mirrors and other highly polished surfaces change the direction in which light is travelling to produce images.

Common plane mirrors are made of thin sheets of glass which are silvered on the back.

Investigating the laws of reflection using light rays

The laws of reflection are true for all reflecting surfaces, for curved mirrors as well as plane mirrors.

y First draw a reflecting line M O M on the paper and then, using a protractor, another line MN at right anglesto the first.

The normal is an imaginary line which is drawn perpendicular to the mirror. A ray which is normal to a mirror

is reflected along its original path.

y Using a protractor, measure and mark several angles of incidence on the paper.The incident ray is the ray striking the mirror. It must be carefully directed at the point O. We say that the line

MN is the normal at the point of incidence.

y Stand a plane mirror upright with its reflecting surface on the line M O M and then shine the ray of lightalong each of the directions in turn,being careful to see that each time the ray strikes the mirror at M.

The angle of incidence, i, is the angle between the incident ray and the normal.

y Mark the direction of each of the reflected rays.y Draw in the reflected rays and measure the angles of reflection, recording these in a table.

The angle of reflection, r, is the angle between the normal and the reflected ray.

Law 1:

The angle of incidence equals the angle of reflection


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Law 2:

The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

The second law means in effect that the rays can all be drawn on a flat sheet of paper. An incident ray whichtravels flat along the surface of a bench will be reflected from the mirror also along the bench surface. If the

mirror were leaning backwards, the reflected ray would leave the bench surface and not be seen on the paper.

WATER WAVES

The general properties of weaves can be examined using water waves. A convenient way to study waves is to use

a ripple tank. This is a shallow container with straight edges, filled with water. A ripple tank can be used to

demonstrate wave phenomena under controlled conditions.

The Stroboscope Principle

A stroboscope chops up the moving picture we see so that our eyes receive separate glimpses of the picture at

regular intervals.

When we use a stroboscope to view something which has a regular repetitive motion, if the frequency of the

glimpses matches the frequency of the repetitive motion then the motion will appear to stop. Persistence of

vision in our eyes joins the sequence of images together giving a smooth stable picture.


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POINT AND EXTENDED SOURCES:

When you drop a pebble into a pond it disturbs the surface of the water and serves as a point source. Point

sources generate circular waves. Circular ripples spread out from the point of disturbance.

All the points on a particular ripple have the same phase. These points of constant phase define a surface known

as a wavefront.A wavefront is an imaginary line which joins a set of particles which are in phase (in step) in a

wave motion.

All the particles along a crest of a wave are in phase and canbe considered as a wavefront. In effect, when we

draw a wavefront we draw the shape of the wave as seen from above, i.e. a plan view. The shape of the wave

seen from the side would be a wave profile.

The distance between successive wavefronts equals one wavelength.

EXTENDED SOURCES:

Extended sources, such a flat bar generate plane waves. If the bar is vibrated at low frequency the waves

produced have long wavelength. On the other hand, if the bar is vibrated at higher frequencies the waves have

shorter wavelength.


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KEY POINTS

y In water of a constant depth, the waves travel at a constant speed, therefore we draw the wavefronts equallyspaced and parallel.

y The direction of travel of the waves, which should be shown, is always at right angles to the wavefronts.y When drawing wave diagrams of reflection or refraction it helps to bear in mind the equivalent light-ray

diagrams. The direction of travel obeys the same laws as the direction of light rays.

y Sources of circular waves and their images formed by reflection should be labelled.

REFLECTION OF STRAIGHT AND CIRCULAR WAVEFRONTS

Both incident and reflected wavefronts are

straight and have equal spacings. The

incident and reflected waves have the same

speed and wavelength.

The angle of incidence i is equal to the angle

of reflection r at all angles. The incident and

reflected wavefronts are at right angles totheir direction of travel.

Reflected wavefronts are circular and appears to come

from R.

The source S corresponds to the object and the virtual

source R of the reflected waves corresponds to the virtual

image formed by a plane mirror. SM = MR and SR is at

right angles to the reflector.


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SOUND

It is found that the reflected sound is loudest when:

1. The angle of reflection r is equal to the angle of incidence i,2. Both tubes lie in a plane which is normal to(at right angles to) the reflected surface.

Based on these observations is found that sound waves do obey the laws of reflection.

When sound waves from a point source strike a plane wall, they produce reflected spherical wavefronts as if

there were an "image" of the sound source at the same distance on the other side of the wall. If something

obstructs the direct sound from the source from reaching your ear, then it may sound as if the entire sound is

coming from the position of the "image" behind the wall. This kind of sound imaging follows the same law of

reflection as your image in a plane mirror.

Law 1:

The angle of incidence equals the angle of reflection

Law 2:

The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

Reverberation:

In a cathedral or large hall, there are many reflecting walls and surfaces, which form multiple reflections and

create the impression that a sound lasts for a long time. A sound produced in a brief moment many linger for

several seconds, only gradually fading away. At each reflection some of the sound energy is absorbed and thereflected sound becomes a little quieter. When many echoes merge into one prolonged sound the effect is known


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as reverberation. Too much reverberation causes sounds to become confused and indistinct making it necessary

to speak very slowly. The sound reflecting and absorbing properties of a room are called its acoustics.

REFRACTION

LIGHT

Refraction is the bending of a wave as it crosses a boundarybetween two media.

A material is transparent ifyou can see through it. Ifyou can see through it, it means that light can travel

through it. Transparent materials include air, glass, Perspex, and water.

Light travels at different speeds in different materials because they have different densities. The higher the

density, the slower light travels. Light travels fastest in space (a vacuum) and a little slower in air. Light moves

noticeably more slowly in glass than in airbecause glass is obviously more dense.

A line drawn at right angles to the boundarybetween the two media (air and glass) is called a normal.

Light which enters a glass block along a normal does not change direction but it does travel more slowly through

the glass and so its wavelength is smaller

y The angle of incidence, i, is the angle between the incident ray and the normal.y The angle of refraction, r, is the angle between the refracted ray and the normal.


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When a ray of light enters a glass block at an angle other than the normal it changes speed, wavelength and

direction as shown above.

In going from a less dense medium (air) to a more dense medium (glass) light bends towards the normal.

This means that i > r (the angle i is greater than the angle r). In going from a more dense to a less dense medium

(glass to air), light bends away from the normal. How much the light bends depends on its colour.

y A medium is considered rare if it is easy for the wave to travel through it. A medium is considered denseif it is difficult for the wave to travel through it.

y For light, air is rare and water is dense. For sound, water is rare and air is dense.y When a wave travels from rare to dense, the wave bends towards the normal.

y When a wave travels from dense to rare, the wave bends away from the normal.

The change in angle of the light ray is the same when it enters and leaves the glass. If the incident ray had

continued without changing direction, then the emergent ray would be parallel to it.

Refraction is the bending of light which occurs when it passes at an angle to the normal from one

transparent material to another.

Literal displacement

This mans the ray is travelling in the same direction but has been shifted sideways when it emerges. This

happens to light whenever it passes through a plane glass window at an angle to the normal.


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THE LAWS OF REFRACTION:

LAW 1:

The incident ray, refracted ray and the normal at the point of incidence all lie in the same plane.

LAW 2: SNELLS LAW

For light rays passing from one transparent medium to another, the sine of the angle of incidence and the

sine of the angle of refraction are in a constant ratio called the refractive index.

Refractive Index:

y The refractive index, n, being a ratio has no units.y The value of the refractive index for a medium indicates how much refraction orbending will occur when

a ray enters it from air. The larger the refractive index the more a ray will bend towards the normal as it

enters the medium.

BE CAREFUL !!!!

y y When we give the refractive index of medium you should understand that it is the relative refractiveindex of that medium.

y y In general, if the density of the medium increases than refractive index of that medium also increases.However, of course there are some exceptions like water.

y y Velocity of the light in a medium is inversely proportional to the refractive index of that medium. If therefractive index increases then velocity of the light decreases.

y y If the light comes perpendicular to the boundary of two different mediums, it does not change itsdirection. Because it is on the normal line of the system. But, the velocity of the light changes since the

density of the medium changes.

y y Refractive index of the medium is also depends on the color of the coming light. For example,refractive index of the medium for violet colors is larger than the refractive index of the medium for other

colors.

y y The angle of refraction of the light coming from the medium having smaller refractive index is smallerthan the angle of incident ray.


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y MIRAGESyyyyyyyyy The mirage is produced by refraction in the air, as shown in the figure above. A mirage can happen when

the air nearer the surface of the ground is less dense than that above. When the Sun has been shining on a

desert or a road and has made the surface very hot, the air next to it is heated and expands, becoming less

dense. The optical density and refractive index of the air gradually increases with height above the

surface as the air gets cooler.

yy Light from a distant object may reach an observers eye by the two paths shown in the figure above with

the result that the object is seen in its true position and also as an inverted image below it. The inverted

image is virtual and is called a mirage.

yy The most likely explanation of the curved ray path is that it is gradually refracted as the light passes

through air of gradually changing density. Approaching the surface, as the air gets hotter and less dense,

the decreasing refractive index bends the ray away from the normal. After skimming along the surface

the ray is graduallybent back towards the normal as it rises through air of increasing density and

refractive index.

y There is a hazy region on the ground between the object and the observer where the surface seems shinyor reflective and a hot dry road may appear to be wet.

y A heat mirage is caused by the refraction of light near the hot ground where the heated air expandsand has a lower refractive index than the colder air above. The mirage is a virtual image of a distant

object, often inverted, which appears in the hazy region close to the ground and may appear much

closer than the real object actually is.

WATER WAVES


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On a hot day the air near the ground is hotso the sound wave bends upwards from thehot air into the cold air (Figure 1).

Fig. 2 In the daytime, the air near the earthsurface is hotter, sound waves are refracted

to the sky.

On a cold night the air near the ground is

cold and so the sound wave bends

downwards. (Figure 2) This is whyyou can

sometimes hear sounds from a long way

awa if the ni ht air is cold.

Fig. 2 In the night-time, the air near the

surface is cooler, sound waves are refracted

to the earth surface.

The refraction of sound in hot and cold air

The speed of sound is greater in hot air than it is in cold air. This is because the molecules of air are movingfaster and the vibrations of the sound wave can therefore be transmitted faster.

This means that when sound travels from hot air to cold air or from cold air to hot air it will refract.

You can notice this on a hot day or a cold night.


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DIFFRACTION

Diffraction is a characteristic displayed by all types of waves. When a wave encounters an obstacle it does not go

straight pass it rather it bends round it. Similarly, when waves encounter a gap the waves spread out the other

side of the gap. This characteristic of waves to bend around obstacles and spread out past gaps is referred to as

diffraction.

The spreading of waves round corners and edges of barriers or through openings or apertures is called

diffraction.

Diffraction is a property which belongs only to waves. The diffraction effects demonstrated in water waves can

also be observed with sound waves and light waves.

LIGHTThe amount of diffraction depends on the size of the barrier or gap and the wavelength. Light displays diffraction

only when it passes through a very narrow gap or slit due to its very small wavelength and this shows that light

displays wave properties.


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WATER

Observations

y When the gap is wide the wavefronts emerge almost straight, apart from a slight curvature and spreadingat the edges.

y When the gap is narrow the straight wavefronts are converted into circular wavefronts, which appear tobe produced by a new point source of waves in the gap.

y The circular wavefronts spread out round the edges of the gap in all directions.y The amount of spreading or diffraction of the waves is greatest when the gap width is similar to the

wavelength of the waves. The diffraction effect is most obvious with water waves when the gap in the

barrier is quite narrow.

SOUND

The street cleaner can hear the sound of the radio even though it is behind an obstacle.

Explanation:

The sound of the radio spreads around the corner of the wall due to diffraction of sound wave.


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As well as reflection and refraction we find that sound waves also shows diffraction effects. Sound waves may

have wavelengths as short as 20 cm or as long as 10 m.

Which wavelengths are diffracted most?

y Waves which have wavelengths similar to the size of the gap they are passing through are diffractedmost.

y A doorway maybe about 1 metre wide which is very similar to the wavelength of many sounds in thelower part of the audible frequency range. So low, low frequency sounds are diffracted a lot and spread

round corners and through openings as well.

y The short-wavelength, high-pitch sounds tend to be more directional because they are diffracted less thanlong-wavelength, low-pitch sounds. When we listen to music from a loudspeaker the high-pitch sounds

can be heard best in front of the loudspeaker and not so well at the side orbehind the speaker. This is

what we mean when we say that high-pitch sounds are more directional, they are not spread out as much

by diffraction.


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EXAMPLES OF DIFFRACTED SOUND

y Sound spreads round corners. You can hear a vehicle approaching from around a blind corner.y Sounds can be heard coming round a building from the far side.y Sound does not com through and open door in narrow beam, but fans out so that it can be heard in any

direction.

y Sound made outside a house comes in through a window and can be heard anywhere inside the room.INTERFERENCE

Interference occurs when two or more similar waves are travelling in the same medium at the same time.

Interference is the name given to the effects which occur when two separate wavetrains overlap. It is intersectingthat waves do not seem to bump into one another, rather they pass through each other and merge or combine

their effects. For, example, the different sounds from a group of instruments played together can be heard

combined and merged; the various sound waves do not collide.

The net effect of two (or more waves) meeting whilst travelling in the same medium is called wave

interference.

Superposition of waves:

y The ability of wave motions to combine together, when they occur together in the same place at the sametime, is known as the superposition of waves.

y Two traveeling waves can pass through each other without being destroyed or even altered.y Interference is what happens when two sets of wavetrains are superposed.y The displacement of any particle caused by overlapping waves is the sum of the separate displacements

caused by each wave at a particular moment.

y The principle of superposition: states that when two (or more) waves moves through a medium, the net(resulting) displacement at any point is the vector sum of the displacement of the individual waves.

WATER

The pattern seen above is called an interference pattern. The two sets of waves combine (interfere) to give:

y Maxima regions of large disturbances, where the crests overlap with crests and troughs with troughs.y Minima regions near zero disturbance, where crests of one wave overlap with troughs of another.


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LINES OF CONSTRUCTIVE INTERFERENCE

The amplitude of the disturbance has increased along the lines, marked X, where the waves are in phase.

Here the displacement at the crest of one wave has been added to the displacement at the crest of the other

wave to produce a larger displacement. This effect is called constructive interference. The two wave

motions have constructed

a larger amplitude wave along the lines marked X.

LINES OF DESTRUCTIVE INTERFERENCE

The water is quite still along several lines, marked O. These are where the waves are in antiphase (out-of-

phase). In effect, the crest of one wave has filled in the trough of the other to produce no displacement of the

water. This effect is called destructive interference. The two wave motions have destroyed each other

along the lines marked O.

What affects the spacing of the interference bands?

y Moving the sources closer together moves the interference bands further apart.y Using longer wavelength moves the interference bands further apart. Longer wavelengths are produced by a

low frequency vibration.

Coherent sources of waves

y Interference effects can be seen only when the two sources of the waves are coherent.y For two sources to be coherent they must have:

o The same frequencyo A constant phase relationship


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This means that the two sets of waves must set off together in step (in phase) or with some other constant phase

difference. This is achieved by fitting two dippers to the same vibrating beam so that their vibrations are kept in

step at all times.

THE INTERFERENCE OF LIGHT WAVES

When light from slits S1 and S2 reaches the screen and gives rise to constructive interference a bright band

results. A bright band occurs if the path difference for wave trains from the two slits is m, where m is a whole

number and is the wavelength of the light.

Darkbands correspond to regions of destructive interference. They occur where the path difference for wave

trains from the two slits is (m + ).

An inspection of the interference pattern reveals:

A centralbright band fringes by two equally spaced darkbands: Each darkband is fringed by two bright bands and so on The intensity of the bands decreases from the centre outwards.

Determining wavelength

Let the distancebetween successive bright (or dark) bands be y. let the perpendicular distance from the double

slit to the screen be L.

Let the slit separation be d. then it can be shown that:

Wavelength () =

=

The conditions for interference fringes

The light waves from the two slits must have exactly the same wavelength and frequency. The two sets of waves must have roughly equal amplitude, otherwise the larger one will swamp the

smaller one and fringes will not be seen.

The two sets of waves must originate from the same light source. The light waves which pass throughthe two slits are said to be coherent when they come from the same source.


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KEYFACTS

i. the central fringes are brighterii. the fringes are evenly spaced

iii. for shorter wavelengths the fringes are closer together and the blue fringes have about half the spacing ofthe red ones

iv. the slit separation has an inverse effect; that is; for slits closer together the fringes are further apartv. Bright fringes occur where crests overlap and cause constructive interference. Here the waves are in

phase: light + light = brighter light

vi. Dark fringes occur where a crest and a trough overlap. Here the waves are out of phase and causedestructive interference; light + light = darkness

Coherent sources of waves

When the double slit is illuminated by a single lamp, each wavetrain passes through both slits at the sametime.

Any change in the phase of the waves, as different wavetrains reach the two slits, happens at both slits. The wavetrains which emerge from the two slits bear the same phase relation to each other at all times

and are therefore coherent waves.

The wavetrains from two separate sources of light would each change in phase independently andrandomly with each new wavetrain emitted from the sources. No constant phase relation can exist

between two sets of waves emitted randomly. Such waves are said to be incoherent and do not produce

interference fringes in fixed positions.

THE INTERFERENCE OF SOUND WAVES

When SOUND WAVEs from two different sources at the same FREQUENCY strike one another, pressure

displacements occur which are the sum and the difference of the AMPLITUDEs of the two waves.

Where the crests of one set of waves coincide with the crests of another set, the amplitude is increased. This is

called constructive interference (the lines indicated by C on the diagram). Where the crests of one set fall on the

troughs of the other, i.e. they are 180 out of PHASE, the two will cancel one another and the resulting

amplitude is decreased. This is called destructive interference orCANCELLATION (the lines indicated byD on

the diagram).


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F

Interference pattern between the wave fronts of two sound sources. Constructive interference is indicated by

lines C, and destructive interference by lines D.

In the figure L1 and L2 are matched speakers which are connected to a signal generator. The signal generator is

emitting a note of constant freqeuncy.

Someone walking along the line EG hears alterante loud sound and no sound at intervals. At a point minwa y

between the two speakers along the line EG is the position of maximum intensitybecause it is equidistant from L

and L2.

L1 and L2 are coherent sources. They are emitting waves of the same frequency ( phase diffrence is constant

throughout). Sound waves from L1 and L2 superpose and interfere constructively and destructively at points

along EG corresponsing to C and D respectively.

Alternating loud and soft sounds are detected as the microphone is moved from left to right.

Explanation:

The two loud speakers are sources of two coherent sound waves as they are connected to the same audio signal

generator.

The alternating loud and soft sounds are caused by interference of the sound wave.

wave phenomena r r d i

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