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# AS and A Level: Waves & Cosmology

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## Redshift

1. 1 When a source of waves is moving relative to an observer (either towards or away) the received waves have a different wavelength to the wavelength transmitted. This is known as the Doppler Effect and we can use it to calculate the speed of a galaxy relative to Earth.
2. 2 Almost all galaxies show redshift, meaning that the wavelength received on Earth is longer than it was when transmitted. It’s called redshift because the wavelength received has moved towards tor even beyond the red end of the spectrum . Redshift implies that the galaxy is moving away from Earth.
3. 3 Blueshift can be observed from ‘nearby’ stars and galaxies.

## Hubble's law

1. 1 Using redshift data from a number of galaxies, Hubble plotted a graph of recession velocity, v, against distance to the galaxy, d. This graph continues to be updated and it shows that v = Hod which is known as Hubble’s law. This means that the speed of recession is directly proportional to the distance to the galaxy.
2. 2 Ho is the Hubble constant and it has a value of about 70 km s-1 Mpc-1, which is equivalent to 2.3x10-18 s-1. 1/Ho= 4.4 x1017 s = 1.4 x 1010 years! This is the age of the universe, about 14 billion years.
3. 3 We can also find an estimate for the size of the (visible) universe, assuming that the maximum expansion speed is the speed of light. Using Hubble law, c = Hod so d = c/Ho = 14 billion light years.
4. 4 The uncertainty over the value of The Hubble constant is becoming smaller as measurements of distance to galaxies improve
5. 5 Since redshift is seen in every direction, the conclusion is that the universe is expanding.

## Fate of the universe

1. 1 The fate of the universe is closely linked to CRITICAL DENSITY. This is a theoretical density that would have enough mass in the universe to keep the expansion of space slowing down forever. The critical density is given by o= 3H2/8 . The universe would be FLAT. An accurate value for H is important, if we want an accurate value for the critical density. Note: H2 means that the percentage uncertainty in H has to be doubled.
2. 2 If the actual density is greater than the critical density, then the universe will stop expanding at some point and then collapse. The universe is then CLOSED. This outcome is known as the Big Crunch.
3. 3 If the actual density is less than the critical density, there is not enough mass to stop the expansion and the universe will continue to expand forever. The universe is OPEN.
4. 4 Determining the actual density is difficult because there seems to be dark matter which we cannot yet detect directly but which can be inferred by the gravitational effects it has. e.g the rotation of galaxies is not consistent with observable mass but with increased mass that may be explained by the presence of dark matter.

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1. ## Wave Coursework

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This will also increase the reliabilty of my results. I will then be able to work out an average, removing any error results out of limit. Before taking any readings of the wave velocity I will measure the length and width of the tray and also see if the tray is flat on the bottom and along the sides. I will do this by placing 1cm depth of water into the tray, taking the measurements at either end and in the centre of the tray.

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2. ## Annihilation Theory

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Matter and antimatter is a collective term given to two identical particles that are of opposite charge. Therefore they are the same with the exception of charge. There opposite charges adhere to the Laws of Attraction, which state that two particles of opposing charge are attracted to each other. On their collision they, theoretically, annihilate each other resulting in a gamma ray (pure radiation). This can be shown by; e+ + e- � ? (A positron plus and electron results in a gamma ray) Equations like these show the fundamental properties of all interactions. Here, the resultant is a gamma ray, which indicates that (considering that gamma particles travel at the speed of light)

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3. ## The Electro magnetic spectrum.

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Their wavelength is usually a couple of centimetres. Stars also give off microwaves. Microwaves cause water and fat molecules to vibrate, which makes the substances hot. Thus we can use microwaves to cook many types of food. Mobile phones use microwaves, as they can be generated by a small antenna, which means that the phone doesn't need to be very big. The drawback is that, being small, they can't put out much power, and they also need a line of sight to the transmitter.

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4. ## Investigate the effect of mass on the extension of a spring.

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* Boss Clamp Hypothesis Using scientific knowledge from that of Hooke's law, I am able to conduct a hypothesis. Hooke's law reveals that the extension is proportional to that of the load, and so if load increases, so does the extension and so stretching the distance. He discovered that extension is proportional to the downward force acting on the springs and so we can use this formula to predict the results. Extension= New length - Original Length Prediction: I predict that the greater the weight applied to the spring, the further the spring will stretch. This is because extension is proportional to load and so if load increases so does extension and so stretching distance To see if my prediction is correct I will experiment, and obtain results using Hookes Law.

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5. ## The effects of the extension of a spring on the time it takes a weight to oscillate.

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So therefore: 1/2 mv2 = maX 1/2 mass x velocity2 = mass x acceleration x extension (distance) The velocity value is the velocity at the mid point which is where the mass final comes to rest after oscillating. The formula can be simplified to: v2 = 2aX Velocity is distance/time and acceleration is force/mass therefore with substituting the formula is: (distance/time)2 = 2 x (Force/Mass) x X Which is equal to: (time2 / distance2) = mass / 2 x force x X The values on the top half of the formula are the constants in this experiment.

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6. ## A report concerning stars and constellations

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Even the Bible makes reference to this famous group. God, while pointing out how all-powerful he was, is purported to have asked Job if he (Job) was able to "loose the bands of Orion" Leo (Lion) The first on the list of Heracles' labours was the task of killing the Nemean Lion, a giant beast that roamed the hills and the streets of the Peloponnesian villages, devouring whomever it met. The animal's skin was impervious to iron, bronze, and stone. Heracles' arrows harmlessly bounced off the lion; his sword bent in two; his wooden club smashed to pieces. So Heracles wrestled with the beast, finally choking it to death.

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7. ## See how one factor affects the period of time a mass on the end of a spring takes to complete one whole oscillation.

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I have chosen to make mass the variable, as this is the easiest variable to use in this experiment. Equipment Here is a diagram of the equipment I will use: Method This is how I will carry out the experiments: 1. Set up the equipment as shown in the diagram 2. Put the mass on the end of the spring (see below for range) 3. Measure the initial displacement (see below) 4. Time 10 oscillations, and divide this answer by 10.

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8. ## Properties of Waves.

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Reflection can be used to guide a laser past obstacles to a receiver. Shiny surfaces such as mirrors are smooth so reflect all light strongly as all the waves pass in one direction only. Rough surfaces look dull as they reflect light in many different directions causing it to scatter. This is called diffuse reflection. If light waves are reflected, the colour of the surface affects the colour of the reflected ray. Concave surfaces are used to focus waves at a point to increase their strength, for example satellites collect radio waves in a dish, then focus the waves on to a point.

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9. ## Astronomy - the urge to explore space.

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It was also found out that the building door and the main door were at an angle of 20�. Astonishingly, this is the exact angle that the same two stars of the constellation had on each other. Until the 11th century the truth about the stars was unknown and there were just a few theories of Ancient Greeks. In the 11th century an Arab astronomer presented the hypothesis of the stars being a lot bigger mass than they appear to the naked eye. This theory was a great new discovery for the astronomers from all over the world and it opened a new era for the astronomers of the future.

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10. ## The Electromagnetic Spectrum.

X-rays are also very high-energy waves and can be dangerous when exposed to them for long periods of time. Gamma waves are less than 10 trillionths of a meter and are even more penetrating then X-rays. The electromagnetic spectrum is not only measure in wavelengths. It is also measured in frequency (cycles per second known as Hertz) and energy involved (measured in electron volts) Objects in space, such as planets and comets, giant clouds of gas and dust, and stars and galaxies, emit light at many different wavelengths. Some of the light they emit has very large wavelengths - sometimes as long as a mile!.

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11. ## Is Space Exploration Worth the Cost?

For example space exploration allows the prediction and management of hurricanes and other natural disasters. Without this many people would suffer from the devastating effects of natural disasters and would not have the opportunity to evacuate an area before a disaster occurred. Important medical developments such as breast cancer detection and biopsy systems, ultrasound scanners and cataract surgery tools have also developed from space technologies. Solar energy, a key alternate energy source to unsustainable fossil fuels, is another technology that has advanced from space [2]. Tax dollars spent on space projects result in jobs, a large proportion of which are high paying, high tech positions.

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12. ## The aim of my coursework is to calculate the wavelength of red laser light using the diffraction grating formula and the Youngs double slit formula.

Insert the 300mm diffraction grating into the slit holder. 4. Place the diffraction grating with the slit holder, 2 meters away from the screen which in my case was a white wall. 5. Mark the spectrum on the wall with a pencil. 6. Measure the length of the distance between the fringes. 7. Take away the diffraction grating and replace it with the double slit. Also remove the two lenses. 8. Repeat the process until all measurements are taken with all the different slits.

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13. ## Refractive index by tracing light rays

A sheet of paper was fixed on the drawing board and the glass block was placed in the middle. The outline of the glass block was sketched by using a sharp pencil. 2. The glass block was removed and 5 straight lines were drawn to represent light rays with angle of incidence varying from 25o to 65o as shown in Fig.1. The lines were labelled as Ray 1 to Ray 5. For each line, the normal is drawn as dotted line and the angle of incidence (i) was measured. 3. The glass block was placed back to the original position.

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14. ## Waves notes

The amplitude of a wave is the greatest distance the medium moves from its normal position. The wavelength of a wave is the distance from any point to the next corresponding point. The period of a wave is the time it takes to move one wavelength. The frequency of a wave is the number of waves that pass in one second. The frequency is the reciprocal of the period. The speed of a wave equals its frequency times its wavelength. A displacement/time graph shows the position of one particle in the medium as the wave passes.

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15. ## Experiment B11: Measuring focal length of lenses

2 fx 20 19 0.05 0.0526 u > 2 fx 30 15 0.0333 0.0667 40 13 0.025 0.0769 50 12 0.02 0.0833 Focal length fu of the convex lens calculated using (1/u)-intercept = = 10 cm Focal length fv of the convex lens calculated using (1/v)-intercept = = 9.756 cm Mean focal length f of the convex lens = = 9.878 cm Uncertainty of the mean focal length f of the convex lens = = 0.122 cm ? Mean focal length f of the convex lens = (9.878 ? 0.122) cm Method (b): Lens displacement method (for a convex lens)

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16. ## Velocity of a wave in a tank at varying depths of water

The wave was allowed to traverse the tray 4 times as opposed to just once because the percentage error was smaller since the error in measurement is fixed and we are measuring over a larger distance. The tray was first filled to a depth of 1cm for the first series of experiments then the depth of the water was increased by 1cm for every series of experiments thereafter. The level of the water was increased to 6cm in depth so 6 different series of experiments were made.

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17. ## Estimating the wavelength of light using a double-slit and a plane diffraction grating

is a multiple n of the wavelength ?, i.e. a sin ?=n?, where n=1,2,3... is known as order number. For small value of ?, Sin?= tan?= s/D Where s is the distance of the fringe from the central line and D is distance from the screen to the double slits. Hence, we have s= nD?/a Consider the nth and the (n+1)th ringes, Fringe separation y= s -s =D?/a --> ?= ay/D Therefore, the wavelength ? can be estimated if fringe separation y is measured. Using a plane diffraction grating A diffraction grating consists of evenly separated opaque and transparent parallel lines.

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18. ## Diffraction Grating with White Light Source

The path difference, BN = 1?(for the first order diffraction) In?ANB, sin = = ? d sin?1 = 1? For the other number of spectrum, we can conclude that d sin?n = n?, where n=0,1,2... d = , for example:the diffraction grating with 300 lines per mm, d = = 3.33 � 10-6m By measuring the length a and b, ?1 can be obtained using the formula tan? = Finally, by substituting the values of ?1 and d into the equation d sin?1 = 1?, the required wavelength can be calculated. Procedures 1. Use the ray box with vertical filament.

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19. ## Measuring the Period of a Pendulum Motion

We than gathered the needed materials listed above. Set-up the clamp on the table which was attached to a rod that was perpendicular to the table. Another clamp was attached at the end of that rod to hold it in place. Next, the wooden ball was measured to be .059 kg and the aluminum ball at .242 kg. The wooden ball was hung from the rod and its measured distance was .888 m. The aluminum ball was then position beside the wooden ball on the same rod and measured at the same distance from the floor; therefore, they would be positioned exactly beside each other.

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20. ## Investigating the relation between wave speed and tension in a slinky spring

The wave will then undergo 'reflection'. The wave will remain within the medium (slinky) but just reverse the direction of travel. A slinky wave which travels to the end of a slinky and back has doubled its distance. That is, by reflecting back to the original location, the wave has travelled a distance which is equal to twice the length of the slinky. There will be two ways in which I can deliver the wave through the medium. I can either create a to and fro motion wave (longitudinal)

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21. ## Hookes law analysis and evaluation

This can be worked out using the equation: K = F / X Graph of my results: The graph that has been plotted (spring stiffness against load) shows that the stiffness of the spring halves when there is single spring but when two are put in series then the stiffness is doubled. It can be seen clearly that the gradient of single spring is almost half of spring in series. Gradient for single spring Gradient for spring in series y = 0.0453x - 0.0068 y = 0.0811x - 0.0059 Also, the graph that has been plotted (spring stiffness against load)

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22. ## How power produced by a solar cell is affected by its distance from a light source.

Then to plot a graph of power against 1/distance this should then give a straight line and hopefully proportionality that is what I wish to prove. To prove that power produce by a solar cell is reciprocal of distance. I placed a light on a table pointed at an array of solar cells mounted on a stand fixed with a clamp. I will move the solar cell closer to the light source and take measurements of the volts and amps that the array produces so I can work out how much power is produced at different distances.

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23. ## investigate how and why the depth of water affects wave speed

There are two types of waves, firstly longitudinal waves, longitudinal waves move in and out (parallel) so when demonstrated with a slinky spring, your hand movement would be moving forwards and backwards as shown below. An example of a longitudinal wave is a sound wave. So for example when we listen to music, the speakers send out longitudinal waves through the air which then reach our ears so we can hear the playing music. The second type of wave is a transverse wave. Transverse waves move up and down so when demonstrated with a slinky spring, your hand movement would obviously be moving up and down as shown below.

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24. ## Investigating Hooke's Law

Hooke's law states that in an elastic material strain is proportional to stress this can be written as this; S ? St Where S = strain and St = stress As part of preliminary work we did an experiment with long and short springs, the purpose of this was to put Hooke's law to the test and determine which spring should be used in the focal experiment. The graphs of my findings are included below; I drew a line of best fit when I had plotted my findings and discovered that the results should be in a straight line and when I draw the line of best fit it should go through the origin of (0,0)

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25. ## The aim of this experiment is to investigate whether the colour of light incident on a medium affects its refractive index.

The ray will have to deviate from its original path and find an alternate, short and straight way through the atoms of the new medium. Any colour of light will have to follow this same path for the shortest and straight way out of the medium, provided the incident angle remains the same. This means that the new medium will bend any colour of light at the particular angle of incidence, by the same value producing the same angle of refraction.

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