# Waves

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• Created by: Jenna k
• Created on: 01-03-14 15:33

## Types of waves

Progressive waves - waves that move away from the source.

Transvers waves - the direction of propergation(movement) is at right angles to the direction of ossilation. This means that it goes up and down, think water and waves on a beach.

Longitudinal waves - the ossilation of this wave is parallel to the direction of pregression. This forms a pulsing movement such as that in sound waves. When all the air particels compact in the ossitaltions this is compression when they spread out this is called rarefaction.

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## Key words of waves

Displacement (m) - the distance travelled in a specific direction, measured in metres

Amplitude (m)- The maximum displacement for its rest postion, measured in metres

Wavelength  (lambda λ). - The distance between equal points on a wave (eg. the trophs or peaks) or the point where one ossilation has occured.

Time period (s)- The time it talks for one complet ossilation to occure.

Frecquency (Hz)- number of ossilations ber unit time.

Phase differance (rad) - The differnce between the patterns of ossilation. When two waves are put together they are said to be in phase (2 Pi)  when they both peak at the same time. They are said to be in anitphase by 180 degress or (pi) when one peaks and the other trophs.

You may do maths you will know this but if you dont then they are just another way to measure angles. All you need to know is that 360 degress is 2 pi rad, 180 degrees is Pi rad and 90 degrees is pi/2 rad. (Pi as in 3.14 used in circles)

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## Wave speed

Wave speed (ms-1) - The speed at which energy is transpered between particles.

You need to knwo how to find the wave speed equation. So, you know that S=D/t. This can be applied to waves and be veocity = wavelength (m)/ time (s) which leads to velocity being meaured in metres per second (ms-1)

You can take it a step forward and appling frequency = 1/time to this equation. This will give you Wave speed (ms-1) - The speed at which energy is transpered between particles. Velocity = frequecy (Hz) x wavelength (m). However this does not lead to the changing of velocityies units.

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## Wave properties

In diagrams rays are used to show the waves. However you only see one part of the wave, which is most likey to be the peak of the wave. This distance inbetween each ray is the wavelength.

Reflection is when a wave bounces of a barrier and travels back towards the source creating an echo. However the wavelength does not change as the distance between rays does not change.

Refraction is when the direction of the wave changes when it is absobed by the medium it is emited to. For example when you put a straw in water it seems to be displaced well this is refreaction.

Diffraction is when the wave passes through a gap and the wave spreads out and changes its formation, however the wavelength does not change.

You need to knwo how this applied to sound and light waves.

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## Electromagetic waves

There are 7 different waves in the elctromagnetic specra, which all travel at the same speed in a vaccume (speed of light [299 792 458 ms-1])

Gamma rays        10¯¹ - 10¯⁹                       Cancer treatment

X-rays                  10¯¹² -10¯⁷                         CT scans, X rays...

UV rays                10¯ - 3.7 x 10¯⁷               Sun tanning, disco lighting

Visible light          3.7 x 10¯ - 7.4 x 10¯⁷    Sight, communication

Infrared               7.4 x 10¯⁷ - 10¯³              Heaters, remote controls

Microwaves          10¯ - 10¯¹                     Mobile phones, microwaves

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There are three different kinds of UV rays UV-A, UV-B and UV-C

UV-A has a wavelength of 315-400 nm. This causes tanning and does not harm us.

UV-B have a wavelength of 280-315 nm. This is the type of UV that causes skin cancer.

UV-C has a wavelength of 100-280 nm. This does not reach the surface of the Earth as the ozone filters it out.

As you can see the smaller the wavelength the more harmful it is to us as humans.

Sunscreens contain chemicals that filter out rays such as UV-B which damage our skin but still lets the UV-A rays through so we still get a sun tan. Then higher the SPF the more protection and filtering there is and the safer you are.

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## Polarisation

Plane-polarised waves

Transverse wave, which wave that had oscillations perpendicular to the direction of motion, are the only wave that can be polarised. Polarised filters, which contain crystalline materials, can cause oscillations in one plane.  So when two polarised filters are placed together at right angles then both planes are polarised and no light is visible through it.

When you put two of the polarisers together the first Polaroid filter is called the Polariser and the second filter is the Analyser. The Analyser is rotated by an angle of θ. The analyser will block out all transverse waves when the two filters are perpendicular to each other.

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## Polarisation continued

You need to know about the equation to work out intensity of the light seen through it at different angles.

Intensity = maximum intensity COS²θ or I=Imax Cos²θ

This is known as Malus’s law. He stated that equation above and that when θ= 90 degrees this is called a Crossed Polaroid.

Uses

Reflection - When waves rebound form a barrier changing direction but raimaing in the same medium.  eg. when you look at a lake on a sunny day you can see a reflection of the sky. This is used in strain analysis. This is really cool and deserves a look up on youtube!

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## Interferance - Superposition

Superposition

when two waves of the same type are in the ame place and the same time then the resultant displacemtn can be found by adding their induvidual displacement.

You need to know how to draw the graphs and add them up.

- When two waves are in phase and are of equale aplitudes and wavelength then you multiple the amplitude by 2 so the graph should be stretched vertical. This does not change where the graph intersects the axis.

-  When two waves of the same wavelength and amplitude are in 180 degree antiphase you will find a patturn. when one has a positive amplitude the other will have a negitive. So the resultant displacement will be zero becasue 1-1 is 0 etc.

- When the two waves are in 90 degrees antiphase then the amplitudes get added together.

In you text book this should be shown otherwise look it up and try drawing them to get the jist.

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## Insterferance and Coherence

Interferance - the addition of two or more waves that results in a new wave patturn.

Constructive interferance is when waves are in phase with wach other and the amplitudes are multiplied by the number of waves.

Distructive interferance is when two waves are in 180 degree antiphase and they cancle each other out.

Coherence - Two waves with a constant wave relationship, So they are always are the same distance away where you are in the wave form.

Waves have to have the same phase differance that is maintained through out the wave form.

Research some coherant and non coherant waves. This will give you an image to see and analyse.

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Light

Sound

Microwave

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## Young Double-slit experiement

In 1801 Thomas Young set up an experiment with a red monochromatic light source which passed through a single slit which defracted the light. It then passed through a second obstical that had two slits in it which defracted the light further. The two sources were coherant becasue they both came form the same source.

This showed 5 differenct points on the wall obersite. The original point of the monochormatic light as well as the two dots on either side of this to show the interferance of the two waves together.

You should research the different tests and result he did they are really interesting. He found the wavelength form this, which you can see in the clearness of the lines of lights that are crated. The red light looks 'fluffy' where as green light is very presise and thiner lines. This shows that red light has a larger wave length than the green light.

Equation - lambda = slit spaceing x the distance between the origen point and its fringe

dvided by distance of the screen to the double slits

lambda = ax/D

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## Multiple slits

By using multiple slits we over come the problem of the 'fluffiness' of the firnges. When we say mulitple slits we mean 300-500 slits er milimetre. So really small.

As the light travels through the secondary slits they are defreacted.This cause the waves to be one wavelength longer than the one above them, making them in phase and thus providing us with a maximum intesity.

This can be given by the equation:

lambda/ spacing between the slits = sin (angle of defraction)

lambda / d =sin (theta)

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## Diffreaction gratings

When a diffreaction grating is placed in the path of a monochromatic beam it splits the light into a number of different maxima. They occure becasue the light splits into 2 lambda, 3 lambda or 4lambda instead of just a straigh line of lambda. The straight line out is called the central maxima. The next line is called second order maxima and so forth.

So combining this with lambda/d=sin(theta) we get an eqaution such as:

n lambda = d sin (theta)

n being the number of the order maxima, d being the spacing of the slits, lambda being the wavelength and theta being the angle between the central maxima and orders.

This is really confusing so see if you can find a video on youtube.

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## Stationary waves and nodes and antinodes

Stationary wave is when the energy is stored rather than transported as progressive waves. Stationary waves are formed by two progressive waves traveling in opersite directions.

On this graph there are two points. One where the waves are either at their crest or troph. These are called Antinodes. The other points, where the waves cross the x axis (wave dispacemnt equales zero) are called the nodes.

The distance between the node and antinode is a quater of a wavelength.

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## Stationary waves experiments

Microwaves > An experiment to measure microwaves would to be to place a metal sheet infront of microwave transmitter. This would result in the microwaves reflecting off the metal and bouncing back forming a stationary wave. Then place a microwave detector in the path of the waves. The signals are particulary strong every half  a wave length. If you multiply the wave length by the frequency of the wave you can find the speed. Wave length = distance from the first maxiumaum to a distant maxiumum / The frequency.

Strings > Frequancey of a strings vibrations are governed by it's mass per unit length, it's tention (Adjusted when tuning) and the length of the string (Adjusted by fingures when playing). Stringed instruments work by transve waves being reflected when it reaches the wood of the bow, thus traveling back on itself and creating a stationary wave.

Air columns > Wind and brass instruments both use the physics of a closed or open tube which is explained on the next pages.

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## Harmonics

When a wave travels down a string it produces a movemnt up and down, like a wave, but this happens increadibly quickly. This is an example.

This is the first harmoic and is half a wave length. This is known as the Fundamental mode of viration.

These are an example of the second and thrid harmoics. Notic that the wavelengths increase in half wavelengths. You also need to know that the frequency of each harmonic is a multiple of the findimental fequancy which is the amount of ocilations per unit time (s). So like i said before there is a interval of half a wavelength

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## Stationary waves in columns

Closed tubes > When air is blown across the opening to the tube it create a progressive wave that move down the tube. When it gets to the closed end, it is relfected and creats a stationary wave. For this to work the wave needs to form a node and each closed end and an anitnode at the opening. This motion causes squeezing and stretching of the interpartical distances at the nodes. However this does not happen to such a large effect at the antinodes. This differance creats pressure changes at the nodes.

Open tubes > The same happens for an open tube. However at the ends of the tube there are antinods and not node. This creats a reflection of the air particals that creats the stationary wave.

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## Measuring the speed of sound

You can find the speed of sound by setting up this experiment.

Place a tuning fork over a tube with its one end immersied in water. (closed end) The vibrations form the tuning fork will vibrate enough to move the air particals. By closing one end with water it allows you to manipulate the length of the tube so you can find the position of resonance.(Resonance is when the sound gets louder as the air in the tube vibrates at the same fequency of the tuning fork).

Once resonance is calculated then the distance form the top of the tube to the level of water can be found. This is the distance form a node to an antinode, as the open end will always end with an antinode and a closed tube will always end with a node.

Speed is then given by V=Frequence x wavelength. So form a node to antinode is a quater of a wavelength so V=F4x.

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