Superposition, Interference and Phase – AS Physics Revision

Wave Collisions

  • When multiple waves occupy the same space, at the same time, they add together
  • This is called superposition
  • The resultant wave’s amplitude could be more or less than their individual amplitudes
  • It doesn’t permanently affect the waves – once they’ve gone through the other waves, they just carry on exactly as they were before the encounter (because we’re in an ideal world where they don’t seem to lose any energy)
  • If two identical waves going the same way, at the same speed, time, etc, superpose, the result will be a wave of double their individual amplitude, but the same frequency
  • However, if one of those waves is half a wavelength ahead of the other, its negative bits are exactly where the other’s positive bits are, so you get a flat line as the result
  • This is called antiphase, and happens when the waves are 180 degrees, or Pi radians, out of phase, as will be covered in the next unordered list

Interference, Coherence and Phase

  • When the resultant is bigger than the individual waves superposing, you have constructive interference
  • When the resultant is smaller, it’s destructive interference
  • Absolute destructive interference, where there’s no wave left (until the superposing waves separate) happens when the superposing waves are in antiphase
  • Complete constructive interference, where the wave doubles, happens when the superposing waves are in phase
  • The wavelength of two coherent waves, and their phase difference, determines how they will interfere (constructively or destructively)
  • Phase difference is the amount by which one wave lags behind another
  • Only waves that are coherent will interfere with each other
  • Coherent waves have a constant phase difference between them
  • Waves have to come from the same source to be coherent (for all intents and purposes)
  • The coherence length is the distance over which the waves are still coherent

Thin Film and Path Difference

  • English: Soap bubble reflects the skyWhen light encounters a thin film some of it will reflect, but some will travel through the film to the other end, and reflect there
  • Because this light has travelled a bit further than the other light, it lags behind the other light, so there is a phase difference
  • This means that it will interfere with the other light as it reflects
  • Since white light is made up of many different colours, with different wavelengths, they all interfere differently, creating a nice light show
  • (Phase changes when during reflection, which adds another layer of complexity to this phenomenon)
  • The thickness of the film, the wavelength of the light, and the angle of incidence hitting the film all have an effect on the pattern
  • If the film is too thick, though, thin-film interference doesn’t work

Path Difference and Wavelength

  • A reliable way to get coherent waves (from the same source) interfere is to them travel different distances
  • The distance one has travelled further than the other is called the path difference
  • If the path difference is equal to the wavelength , two wavelengths, three wavelengths, or so on, the waves are in phase and will interfere constructively
  • If the path difference is equal to half a wavelength, 1.5 wavelengths, 2.5 wavelengths, or so on, the waves are in antiphase and will interfere destructively
  • In other words, if the path difference = nλ, where n is an integer (and lambda is the wavelength, obviously), the waves are in phase
  • And, if the path difference = nλ + 0.5λ, or λ(n+0.5), then the waves are in antiphase
  • They can, of course, be somewhere between antiphase and completely-in-phase (and usually will be) – leading to patterns of increasing and decreasing amplitude in the interference pattern

Phasors

  • Phasors are a way of working out superposition, and representing phase difference
  • They’re more important in quantum theory, but are used for waves, too
  • They’re arrows, which represent the phase at a point on the wave as a direction
  • They have amplitude, which is the length of the arrow (in a similar way to how vectors can be represented as arrows)
  • As a wave goes along, the phasors rotate ANTICLOCKWISE
  • They start from the right, pointing to three o’clock
  • Each phasor is slightly behind the one in front of it, in its rotation
  • When you’re working out superposition, instead of adding the amplitudes at each point, you can add the phasor arrows at each point, to get a resultant
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About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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One Response to Superposition, Interference and Phase – AS Physics Revision

  1. sahiljhamb says:

    library computer room is free

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