Waves

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  • Waves
    • E.M spectrum
      • All e.m waves have some properties in common.
        • They all travel at the speed of light - 299800000 metres per second in a vacuum.
        • They are transverse waves with vibrating electric and magnetic fields at right angles to each other and the direction of travel.
        • They can be reflected, refracted and diffracted and can undergo interference.
        • They all carry energy and they can be polarised.
      • Some properties vary across the e.m spectrum.
        • Energy is directly proportional to frequency.
        • The higher the energy, in general the more dangerous the wave.
        • The lower the energy of a e.m wave the further from the nucleus it comes from, e.g gamma rays come from inside the nucleus, whilst X- rays to visible light come from energy-level transmissions in atoms. Infrared and microwaves are associated with molecules. Radio waves come from oscillations in electric fields.
      • Different types of e.m wave have different effects on the human body. Radio: No effect. Microwaves: Absorbed by water, can cook human body. Infrared: Heating. Excess heat harms the body's systems. Visible: Used for sight. Too bright a light can damage eyes. UV: tans the skin. Can cause skin cancer and eye damage. X-ray and gamma ray: Cancer due to cell damage. Eye damage.
      • UV light
        • UV-A: Lowest frequency, least damaging.
        • UV-B: Most damaging, causes cancer and sunburn.
          • Sunscreen protects from UV-B light, and has tiny particles of zinc oxide and titanium dioxide to block UV-A.
        • UV-C: Ionising, can cause cell mutation or destruction, but mostly blocked by the ozone layer.
    • Nature of waves
      • Transfers energy away from its source
      • Key features of a wave
        • Displacement - how far a point on the wave has moved from its undisturbed position (metres)
        • Amplitude - Maximum displacement (metres)
        • Wavelength - the length of one whole wave from crest to crest or trough to trough. (metres)
        • Frequency - the number of vibrations per second passing a given point (hertz)
          • Frequency = 1 divided by period
        • Phase difference - the amount by which one wave lags behind another wave. (Degrees or radians)
      • Reflection and refraction
        • Reflection -  The wave is bounced back when it hits a boundary.
        • Refraction - The wave changes direction when it enters a different medium
      • Intensity
        • Intensity is a measure of how much energy a wave has.
        • Intensity is the rate of flow of energy per unit area at right angles to the direction of travel. (Watts per metre squared)
        • Proportional to the square of the amplitude of the wave.
      • Wave equation
        • Speed of a wave = wavelength multiplied by frequency.
    • Longitudinal and transverse
      • Longitudinal waves have vibrations along the direction of travel.
      • Transverse waves have vibrations at right angles to direction of travel.
      • Polarised waves oscillate in one direction only. Only works for transverse waves.
        • A polarising filter transmits vibrations in only one direction. Two polarising filter at right angles to one another then no light gets through.
        • When light reflects it is partially polarised and changes with the orientation of the filter.
        • Materials can rotate the plane of polarisation.
        • Malus' Law: The intensity of the transmitted light is proportional to the amplitude squared.
    • Superposition and Coherence
      • Superposition happens when two or more waves pass through each other.
        • When two waves cross the displacements of the waves combine.
        • The principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements.
      • Interference can be constructive, in which two crests or two troughs combine to make a bigger one, or it can be destructive, in which a crest meets a trough of equal size or vice versa and cancels out.
        • But if the crest and trough are not of equal size the destructive interference isn't total.
      • In phase means in step - two points in phase interfere constructively.
        • Two points on a wave are in phase if they are both at the same point in the wave cycle.
      • To get interference patterns the two sources must be coherent - when two sources have the same wavelength and a fixed phase difference between them.
      • Constructive or destructive interference depends on the path difference.
        • The amount by which the path travelled by one wave is longer than the path travelled by the other wave is called the path difference.
        • Constructive interference occurs when: Path difference is equal to n (an integer) multiplied by wavelength.
        • Destructive interference occurs when path difference is equal to (2n+1) multiplied by wavelength halved.
    • Stationary waves
      • You get standing waves when a progressive wave is reflected at a boundary.
        • A standing wave is the superposition  of two progressive waves with the same wavelength, moving in opposite directions.
      • Standing waves in strings form "oscillating loops" separated by nodes.
        • Each particle vibrates at right angles to the string. Nodes are where the amplitude of the vibration is zero. Antinodes are points of maximum amplitude.
        • If a standing wave is vibrating at its lowest resonant frequency (fundamental frequency) with a node at each end is the first harmonic. It is half a wavelength long.
        • The second harmonic has a node at each end and a node in the middle and is twice the fundamental frequency. It is one wavelength long.
        • The third harmonic has three times the fundamental frequency and 1 and a half wavelengths fit on the string.
      • The notes played by string and wind instruments are standing waves. Transverse standing waves form on the strings of stringed instruments. When you flick the string waves are sent out in both directions and reflected back at both ends.
      • Microwaves reflected off a metal plate set up a standing wave.
      • You can use standing waves to measure the speed of sound by finding the nodes in a tube of water and find the shortest distance from the top of the tube and the water level that the sound from a tuning fork with a certain frequency resonates. From this you can multiply the distance by 4 after adding an end correction and using v=f multiplied by wavelength.
    • Diffraction
      • Waves go round corners and spread out of gaps. Diffraction is the way that waves spread out as they come through a narrow gap or go round an obstacle.
        • When a wave meets an obstacle you get diffraction around the edges. The wave is blocked behind the obstacle. The wider the obstacle compared with the wavelength, the less diffraction you get.
      • With light waves you get a pattern of light and dark fringes if the wavelength of a light wave is about the same size as the aperture. The pattern has a bright central fringe with alternating dark and bright fringes on either side of it.
        • The pattern is similar with electrons, leading to the notion of wave-particle duality.
    • Two-Source interference
      • Demonstrating two source interference is easy with sound and water because their wavelengths can be measured easily, if you have two coherent sources.
        • For light doing this is harder. Young's double slit experiment managed to do it by using monochromatic light with one wavelength and that is coherent. You shine it in between two slits with a shorter wavelength than the light so that it is diffracted and shows a pattern of alternating light and dark fringes.
          • You can work out the wavelength using Young's double slit formula, which states that the wavelength is equal to the fringe spacing multiplied by the slit spacing all divided by the distance between the slits and the screen.
          • Young's experiment proved the wave nature of light, by confirming Huygens' theory that light is made up of waves, unlike Isaac Newton who thought of it as particles.
    • Diffraction gratings
      • Interference patterns get sharper when shone through more slits, by doing Young's experiment but with more slits. The bright bands in the pattern are brighter and narrower, and the dark bands are darker.
      • Monochromatic light on a diffraction grating gives sharp lines. The line of maximum brightness is the zero order line. The lines either side of it are first order lines, and the next pair out are second order lines, and so on.
        • For a grating with slits distance d apart the angle between the incident beam and the nth order is given by: distance d multiplied by the sine of the angle equals the number of orders multiplied by the wavelength.
          • You can draw general conclusions from this formula. If wavelength is bigger, the sine of the angle is bigger and the angle is bigger. If d is bigger, then the sine of the angle is smaller. Values of sin theta greater than 1 are impossible, so for a certain n an answer of more than one tells you that order does not exist.
      • Shining white light through a diffraction grating produces spectra with the zero order in the centre white and the first order, second order etc. show all the colours of the rainbow spread out due to the different wavelengths of light in white light. Violet is closest to the zero order whilst red is the farthest. The zero order is white as all the wavelengths pass straight through.

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