• 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 (f_o) is different from the actual frequency (f_s).
  • f_o = ^f_sv/_{v ± vs}
  • where v is the speed of the wave and v_s 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