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General Waves - Types and Properties

  • Waves transfer energy without transferring matter.
  • Displacement is the distance of a point form it undisturbed position.
  • Frequency is the number of waves passing any point per second; it is the number of oscillations per unit time, measured in Hertz (Hz).
    • Frequency = 1/Period = 1/T
  • Period is the time taken for one complete oscillation, in seconds.
  • Wavefront is the peak of a transverse wave or the compression of a longitudinal wave.
  • Wave Speed is the speed at which the waveform travels in the direction of the propagation of the wave; it is how fast the wave travels, measured in m/s
    • Speed (m/s) = Frequency (Hz) × Wavelength (m)
    • v = fλ
  • Wavelength is the distance between a point on one wave to the equivalent point on the next wave, in meters.
  • Amplitude is the maximum distance a wave moves from its rest position when a wave passes.
  • Progressive waves transfer energy from one position to another.
Transverse and Longitudinal Waves

Refraction
  • Speed and wavelength is reduced but frequency stays the same and the wave changes direction.
  • Waves slow down when they pass from a less dense to a more dense material and vice versa.
  • When a wave is slowed down, it is refracted towards the normal (i > r)
  • When a wave is sped up, it is refracted away from the normal (i < r)
  • Deep water is denser than shallow water.
Reflection

  • Waves bounce away from a surface at the same angle they strike it.
  • Angle of incidence = Angle of reflection
  • Speed, wavelength and frequency are unchanged by reflection.
Diffraction

  • Waves bend around the sides of obstacles or they spread out as they pass through a gap.
  • Wider gaps produce less diffraction.
  • When the gap size is equal to the wavelength, maximum diffraction occurs.
Deducing Wave Equations
  • Speed = Distance/Time
  • Distance of 1 wavelength is λ and the time taken for this is T
  • ∴ v = λ/T = λ (1/T)
  • but f = 1/T
  • ∴ v = fλ
Phase Difference
  • Phase difference between two waves is the difference in terms of a fraction of a cycle or in terms of angles.
Intensity
  • Rate of energy transmitted per unit area is perpendicular to the direction of the wave propagation.
  • Intensity ∝ (Amplitude)2
  • Intensity = Power/Cross Sectional Area
Polarization
  • Polarization causes the vibration of particles to be confined to one direction in the plane normal to the direction of the propagation.
  • Polarization can occur in transverse waves but not in longitudinal waves.
The Doppler Effect
  • The Doppler Effect arises when the source of the waves moves relative to the observer.
  • It can occur in all types of waves, including sound and light.
  • The Source Stationary Relative to the Observer:
  • The Source Moving Towards Observer:
  • The Source Moving Away from Observer:
  • A change in wavelength leads to a change in frequency.
  • The observed frequency (fo) is different from the actual frequency (fs).
    • fo = fsv/v ± vs
    • where v is the speed of the wave and vs is the speed of the source relative to the observer.
Electromagnetic Waves

  • All electromagnetic waves:
    • travel at the speed of light (3 × 108 m/s)
    • travel in free space (do not need a medium to travel)
    • can transfer energy
    • are transverse waves
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