PH2

PH2

1. Waves

   • Longitudinal Waves
     • A wave in which the particle oscillations are parallel to the direction of travel (propagation) of the wave
     • Examples
       • Sound waves
       • Earthquake "P" waves
       • Compression waves in a slinky spring
   • Transverse Waves
     • A wave in which the particle oscillations are at right angles to the direction of travel (propagation) of the wave.
     • Examples
       • Light and other Electromagnetic Waves
       • Earthquake "S" waves
       • Waves in a stretched string
   • Key Words
     • Amplitude = maximum displacement from equilibrium position
     • Period = time taken for one complete cycle of oscillation
       • Period = 1/frequency
     • Frequency = the number or cycles of a wave that pass a given point in one secon
       • Frequency = 1/period
       • Measured in Hz
     • Wave speed = the speed of a wave propogation
       • Wave speed = frequency x wavelength
     • Wavelength = The minimum distance between two points on a wave oscillating in phase
     • Monochromatic Light = continuous oscillation of almost a single frequency
     • Coherent light = monochromatic light with wavefronts continuous across single beam
     • Coherent source = wave sources which have a constant phase difference between them (and the therefore must have same frequency
     • Diffraction grating = a flat plate which is opaque except for thousands of straight, parallel, equally spaced slits
   • Phase and Phase difference
     • Relationship between waves is called phase
     • Difference in position of two points on a wave is called phase difference
     • In phase = at the same point in their oscillations at the same time
   • Polarisation
     • A transverse wave can oscillate in any direction
       • However a polarised was can only oscillate in one direction
     • You polarise a wave using a filter
   • Interference
     • Principle of superposition
       • When waves from two or more sources travel through the same region, the resultant displacement at any point is the vector sum of the displacement of the individual waves
     • Two types of interference
       • Constructive interference
         • When two waves are in phase, the result would be a wave where the amplitude of the final wave is the sum of the amplitude of the two waves
       • Destructive interference
         • When two waves are out of phase, the amplitudes cancel each other out
     • Interference pattern is what is observed when superposition has occurred, beams of high amplitude and beams of low amplitude
     • Path Difference
       • Path difference = s1x-s2x
         • Constructive interference = integer number (n) of wavelength
         • Destructive interference = n+1/2 wavelengths
   • Diffraction
     • Diffraction = the spreading out of waves when they meet obstacles (or pass through gaps) such as the edges of a slit
     • Diffraction is greater when the gap size is closest to wavelenght
       • Diffraction reaches a maximum when gap size = wavelength
     • With diffraction, observed pattern shows a very bright central fringe with thinner less bright fringes spreading round
       • Formula is: width of central fringe = (2wavelength x distance from slit to screen) / width of slit
   • Thomas Young's Fringes experiment
     • When path difference is integer number of wavelengths, waves from the slit arrive in phase and interfere constructively
     • When the light from a single slit or laser (and therefore the waves leaving the slits) is coherent, their phase difference is constant
     • Young noticed a pattern of bright and dark fringes, and recognised this as part of an interference pattern
     • He deduced that light was a wave-like radiation which supported a previous theory
     • Young deduced that:
       • Wavelength = (slit separation x fringe spacing) / distance between screen and laser
     • For it to work
       • Light must be monochromatic (one colour or frequency)
       • Single slit used to obtain coherent light source (not needed if laser is used)
       • Double slit - typical width 0.1mm and typical separation 0.5mm
       • Double slit to fringe distance - screen typically 1m away, but distance can be shortened if microscope is used to observe fringes
     • Too inaccurate
       • The fringes are not sharp, bright fringes fade gradually into dark
       • Bright fringes not very bright
       • Fringe separation too small
   • Diffraction grating experiment
     • When a parallel beam of monochromatic light is incident normally with the grating, the light is transmitted in certain directions only
       • This happens because
         • The light is diffracted by each slit in the grating
         • The diffracted light from adjacent slits reinforces in a few directions, in all other directions cancellations occur
         • A diffraction grating may consist of thousands of slits per cm and so diffract light very well
         • The slits are very narrow, so the diffracted waves spread right round and interfere to produce beams
         • These produce fringes like in the double slit experiment but a lot further apart as the slits are closer together
     • Diffraction Grating Equation
       • Grating spaces (d) x sin (angle between beam and zero order) = beam order number (n) x the wavelength of light
       • Number of slits per metre
         • Number of slits per metre (N) = 1 / grating spaces
   • Stationary Waves
     • Stationary waves are formed when two progressive waves of equal amplitude and frequency travel in opposite directions
       • This is usually achieved by superposing a wave with its reflected incident wave
       • They interfere to produce a wave that doesn't seem to move, there is no transfer of wavelength
     • Amplitude is constant for progressive waves as we go through the medium, but it goes up and down regularly to form a stationary wave
       • Amplitude drops to zero at nodes and a maximum at antinodes
     • Nodes and Antinodes
       • The intermodal distance is half a wavelength
       • Between one node and the next, all particles oscillate in phase, but there is a phase reversal at each node
       • Nodes
         • A node is a point on a stationary wave where the amplitude is at a minimum, usually zero
         • It is caused by destructive interference
         • They happen every half wavelength
       • Antinodes
         • Antinodes are points within stationary waves where the amplitude is at a maximum
         • They are caused by constructive interference
         • They are spaced half a wavelength apart
     • Stationary waves on strings
       • Fundamental mode (first harmonic)
         • Lowest frequency that can produce a stationary wave
         • Length of the loop (L) is equal to half the wavelength
         • lambda/2=L so lambda=2L
         • f=v/lambda so f=v/2L
       • Second harmonic
         • Second lowest frequency that can produce a stationary wave
         • The length of the loop is equal to one wavelength
         • Lambda=L so f=v/L
       • Each time goes up by half integer of wavelength
     • Other types of standing/stationary waves
       • Any type of progressive wave can have a corresponding stationary wave
         • For stationary waves in pipes there are nodes at closed ends and antinodes at open ends
       • Tubes closed at one end
         • First harmonic
           • L=1/4 lambda
           • f=v/4L
         • Third harmonic
           • L=3/4 lambda
           • f=3v/4L
         • Fifth harmonic
           • L=5/4 lambda
           • f=5v/4L
       • Tubes open at both ends
         • First harmonic
           • L=1/2 lambda
           • f=v/2L
         • Second harmonic
           • L=lambda
           • f=v/L
         • Third harmonic
           • L=3/2 lambda
           • f=3v/2L
   • Refraction
     • Refraction is change in direction of propagation of a wave due to a change in its transmission medium
     • If V2>V1 then the direction of travel bends away from the normal
       • With a smaller refractive index, it bends away from the normal and with a larger refractive index it bends towards the normal
         • Sinx1/Sinx2=v1/v2
     • Refractive index
       • A number which tells you how fast light will travel through in that medium relative to a vacuum
         • n = (speed of light in a vacuum) / (speed of light in the medium)
       • Or n1sinx1=n2sinx2 because sinx1/sinx2=n1/n2 is equivilant to sinx1/sinx2=n2/n2
         • Because nv=c and n1v1=n2v2 so v1/v2=n2/n1
     • Snell's Law
       • sinx1/sinx2=v1/v1=n2/n1