Waves - Chapter 11

Waves - Chapter 11

1. Basics

   • Waves are produced by oscillation
     • Oscillation is the constant to and throe motion
   • Waves transmit through different substances (or mediums)
   • Primary waves are longitudinal and fastest
     • Secondary waves are transverse and slower
   • A transverse wave oscillates 90 degrees to the direction of travel
   • A longitudinal wave oscillates in the same direction as the wave
     • This wave is made up of lots of compressions and rarefactions
       • Compressions = high density and high pressure
       • Rarefactions = low density and low pressure
   • Waves seem to be progressing but actually the particles say in the same place and oscillate to transfer their energy
   • Superposition
     • This is when you are at a point listening to music and if the waves are anti phase then they are destructive and there are no waves (so you can't hear anything), but if they are in phase they are constructive and there are waves and you can hear sound

2. For calculations

   • Electromagnetic waves travel at 3x10^8
     • Sound travels at 340ms^-1
   • Frequency = 1/time period (s)
     • The time period is the time to complete an oscillation
   • Speed = frequency x wavelength
   • C = Sin^-1*1/n

3. Intensity

   • Intensity is directly proportional to 1/r^2
     • It is also directly proportional to A^2
       • Therefore, if you half the amplitude you half the speed and hense waves have 1/4 of energy and intensity
   • Intensity = Power/Area
   • Inverse square law
     • I = P/4πr^2
       • Power = watts/time
   • Unit is Wm^-2
   • The radiant power passing through a surface per unit area

4. Superposition

   • This is a combination of wave displacements when two or more waves meet and combine
   • This can be observed (e.g.) when coherent waves from 2 sources meet and combine to form an interference pattern

5. Refractive index

   • n = speed of light in vacuum/speed of light in medium
   • n2 = sine(angle in air)/sine(angle in medium 2)

6. Total Internal Reflection

   • This can be used in optic fibres to pass large amounts of information as light (in binary)
   • The two conditions for this are
     • The light must be travelling through a medium of a higher refractive index as it strikes a boundary with a lower refractive index
     • The angle at which the light strikes the boundary must be above the critical angle
   • nSinC = n(air)Sin90
     • SinC = 1/n

7. Wave phase

   • Phase is a particular point in the cycle of a wave form
     • This is usually measured as an angle
   • Two waves are said to be in phase if displacement of points on each wave is the same (phase difference of 0 degrees)
     • Waves are anti-phase if the displacement points are opposite (i.e. phase difference of 180 degrees
   • A wave is can be seen as a circle as its draw out, 2π radians is a full circle

8. Refraction

   • Waves can slow down when changing medium
     • The wavelength decreases (just like the speed) and therefore light bends
       • Red light is slowest and blue light is fastest
         • Red light will therefore bend the most and blue light the least
   • If waves slow down they refract to the normal
     • If waves speed up they refract away from the normal
   • Water waves
     • Speed of water is affected by the change in the depth
     • When a water wave enters shallower water, it slows down and the wavelength gets shorter

9. Waves

   • Progressive waves
     • This is an oscillation that travels through matter
       • It transfers energy but no matter
       • Particles vibrate in plane parallel to the direction of energy transfer
       • A displaced particle experiences a restoring force from its neighbour
     • e.g. sound
   • Transverse waves
     • The oscillations are perpendicular to the direction of energy transfer

10. Polarisation

    • Malus' Law
      • Intensity is proportional to cos^2 of the angle
    • Polarisation means the particles oscillate along in one direction only
    • Light from an unpolarised source (like a filament lamp) is made of oscillations in many possible planes
    • Partial polarisation
      • When transverse waves reflect off a surface they become partially polarised
      • More waves oscillating in one particular plane
    • Polarisation of EM waves
      • Most natural EM waves are unpolarised
      • Polarisers can stop all vibrations apart from the direction you want them in

11. Phase difference

    • This describes the difference of the displacement of particles on a wave
    • If two waves are in phase, the phase difference is 0
    • If two particles are separated by a whole wavelength they are said to be 360 degrees out of phase (or 2pi radians)
    • If two particles are anti phase then the phase difference is 180 degrees

12. Reflection

    • Angle of incidence = angle of reflection

13. Diffraction

    • How much a wave diffracts depends on the size of the wavelength and gap
      • If gap size = wavelength then maximum diffraction
    • When waves pass through a gap or travel around an obstacle they spread out

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