Waves

• Progressive waves transfer energy from one place to another, but not matter.
• When a wave travels through a medium, particles are moved from their equilibrium.
• In a transverse wave, the particle vibrations are perpendicular to the direction of the wave.
• In a longitudinal wave, the particle vibrations are parallel to the direction of the wave.
• Transverse waves have peaks and troughs, where the particles are at their highest and lowest points respectively.
• Longitudinal waves consist of compressions and rarefactions, where the particles are close together and spread out respectively.
• In a wave, displacement is the distance between a particle’s equilibrium and its current position. Amplitude is its maximum displacement on the wave.
• The wavelength of a wave is the distance between the same point on two consecutive waves.
• The period of a wave is the time taken for one oscillation to occur.
• The frequency of a wave is the number of full waves passing a point per second.
• The speed, frequency and wavelength of a wave are related by the equation $v=$$f\lambda$.
• The frequency and period of a wave are related by the equation $f=$$\frac 1 T$.
• A wave can be represented by distance-displacement graph, which can be used to find wavelength and amplitude of a wave.
• Phase difference is the difference between the displacements of particles on one or multiple waves, and is measured in degrees or radians.
• If particles reach their maximum positive and negative displacements at the same time, they are in phase.
• If one particle reaches its maximum positive displacement as the other reaches its maximum negative displacement, then they are antiphase, with a phase difference of 180 degrees.
• The phase difference between two points on a wave is related to the distance between the points and the wavelength by $\phi =$$\frac x \lambda \times 360$.
• A wave can be represented by a displacement-time graph, which can be used to find the period of the wave and its amplitude.
• Reflection is when a wave changes direction at the boundary between two media.
• The angle of incidence is always equal to the angle of reflection.
• No properties of the wave change when it is reflected.
• Refraction is when a wave changes direction and speed as it passes through one medium into another.
• There is some reflection when a wave refracts.
• If a wave slows down, it will bend towards the normal, and if it speeds up, it will bend away from the normal.
• When entering a denser medium, sound waves usually speed up, and EM waves usually slow down.
• The speed and wavelength of a wave change, but its frequency remains constant when it refracts.
• When a water wave enters shallower water, it slows down and its wavelength decreases.
• When waves pass through a gap and spread out, this is called diffraction.
• When a wave diffracts, its speed, wavelength and frequency remain constant.
• A wave diffracts more when the size of the gap is close to its wavelength.
• Polarisation only allows particles to oscillate on one plane.
• Only transverse waves can be plane polarised, as longitudinal waves only cause particle vibrations parallel to the direction of energy transfer.
• When a wave is reflected off a surface, more waves oscillate in one plane, so the wave is partially polarised.
• Intensity is the power passing through a unit area.
• Intensity can be found using the equation $I=$$\frac P A$.
• Intensity is inversely proportional to the square of the distance from the source.
• Intensity is directly proportional to the square of the amplitude of the wave.
• Electromagnetic waves can travel through a vacuum, as they do not need a medium.
• EM waves are electric and magnetic fields oscillating perpendicular to each other.
• The standard wavelengths of the EM waves in metres are:

  • Radio - $10^6 - 10^{-1}$
  • Microwaves - $10^{-1} - 10^{-3}$
  • Infrared - $10^{-3} - 7\times 10^{-7}$
  • Visible - $7\times 10^{-7} - 4\times 10^{-7}$
  • Ultraviolet - $4\times 10^{-7} - 10^{-8}$
  • X rays - $10^{-8} - 10^{-13}$
  • Gamma - $10^{-10} - 10^{-16}$