Waves

• A progressive wave transfers energy without transferring material and is made up of particles of a medium oscillating.
• Amplitude is a wave's maximum displacement from the equilibrium position, and is measured in metres.
• Frequency is the number of complete oscillations passing through a point per second, and is measured in hertz.
• Wavelength is the length of one whole oscillation, and is measured in metres.
• Wave speed is the distance travelled by the wave per unit time, and is measured in metres per second.
• Phase is the position of a certain point on a wave cycle, and is measured in either radians, degrees or fractions of a cycle.
• Phase difference is the difference in position of a particle or wave, and is measured in either radians, degrees or fractions of a cycle.
• Period is the time taken for one full oscillation, and is measured in seconds.
• Two points on a wave are in phase if they are at the same point on the wave cycle and have a phase difference of two pi.
• Twi points on a wave are in antiphase if they have equal but opposite velocity and displacement and have a phase difference of one pi.
• The speed of a wave can be related to frequency and wavelength by c = f x $\lambda$.
• Frequency and time period are related by f = 1 / T.
• Transverse waves oscillate perpendicular to the direction of energy transfer and can travel in a vacuum. Longitudinal waves oscillate parallel to the direction of energy transfer, cannot travel in a vacuum, and are composed of compressions and rarefactions.
• A polarised wave only oscillates in one plane, and this can only occur with transverse waves. Polaroid sunglasses reduce glare and TV and radio signals are polarised so an aerial must be aligned in the correct plane.
• Superposition is where the displacements of two waves are combined as they pass each other causing constructive and destructive interference.
• A stationary wave is formed from the superposition of two progressive, coherent waves travelling in opposite directions, and stores energy instead of transferring it.
• Coherent waves have the same frequency and a constant phase difference (same wavelength and amplitude).
• On a stationary wave, antinodes are regions of maximum displacement and are where the waves meet in phase, and nodes are areas of no displacement and are where the waves meet in antiphase.
• The lowest frequency upon which a stationary wave forms is the first harmonic, the frequency of which can be calculated by f = (1 /2 L)root(T / mu), where L is the length of the wave, T is the tension and mu is the mass per unit length.
• Path difference is the difference in the distance travelled by two waves.
• Young's double slit experiment demonstrates interference of light from two coherent sources. Light fringes are formed when the light meets in phase, has a path difference of a whole number of wavelengths and so interferes constructively, and dark fringes are formed when the light meets in antiphase, has a path difference of a whole number plus one half of a wavelength and so interferes destructively.
• Young's double slit experiment is w = ( $\lambda$ x D ) / s, where w is the fringe spacing, $\lambda$is the wavelength, D is the distance between the slits and screen, and s is slit separation.
• Using white light instead of monochromatic light in Young's double slit experiment gives wider maxima and a less intense diffraction pattern with a central white fringe and alternating bright fringes which are spectra, with blue closest to the central maximum.
• Diffraction is the spreading out of waves when they pass through or around a gap, with the greatest diffraction occurring when the gap is the same size as the wavelength.
• Light can be diffracted through a single slit onto a screen, forming an interference pattern with an intense central fringe twice the width of all the other, significantly less intense, fringes.
• A diffraction grating is a slide with many equally spaced slits very close together and the angle of diffraction of maxima is given by sin $\theta$ = (n x $\lambda$)/ d, where n is the order of the maxima, $\lambda$ is the wavelength and d is the distance between the slits. The max value of sin $\theta$ is one so any values of n that give sin $\theta$ as more than one are impossible.
• The refractive index, n, of a material measures how optically dense it is, ie how much it slows down the speed of light. It can thus be found by n = c / v.
• When a wave enters a different medium, Snell's law can be used to find the angle of refraction: $n_1$ sin $\theta_1$ = $n_2$ sin $\theta_2$.
• The critical angle is where the angle of refraction is exactly 90 degrees, and any larger angle of incidence will cause total internal reflection, given the refractive index of the material at the boundary is less than the incident refractive index.
• Optical fibres have an optically dense core surrounded by a cladding with lower refractive index to allow total internal reflection to occur. The cladding also protects the core and prevents signal degradation through light escaping the core.
• Signal degradation in an optical fibre can be caused by light escaping the core, absorption of the signal's energy by the fibre and dispersion of the light, all leading to a loss of information. A cladding with low refractive index, a highly transparent, narrow core, monochromatic light, and repeaters can be used.
• The two types of dispersion in an optical fibre is modal and material, and both lead to pulse broadening. Modal is caused by light entering the core at a variety of incident angles. Material is caused by using light of a variety of wavelengths as they will have different speeds. While red light refracts less, it is faster so reaches the end of the fibre first.