PHYA2 - Waves

  • Created by: Franklin
  • Created on: 29-04-14 22:07

Introduction to Waves

Waves the pass through a substance are vibrations

  • Sound waves and seismic waves are examples of mechanical waves: vibrating particles cause nearby particles to vibrate and so on
  • EM waves do not need a substance in order to vibrate

Londitudal Waves

  • They vibrate parallel to the direction of propagation

Transverse Waves

  • They vibrate perpendicular to the direction of propagation
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Transverse waves are plane-polarised if the vibrations are only in one plane

  • Longditudal waves cannot be polarised
  • If unpolarised light passes through two filters and one filter is said to be crossed relative to the other then the light intensity is at a minimum
  • Light coming through the first filter is blocked by the second because the second is at 90 degrees to the first
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Wave terminology

  • Displacement of a vibrating particle - the distance and direction of the particle from its equilibrium position
  • Amplitude - The MAX displacement of a vibrating particle (this can be positive or negative i.e crest/trough)
  • Wavelength - the least distance between two adjacent vibrating point (e.g. trough-trough)
  • Period - time for one complete wave to pass a fixed point

Period = 1/f

Wave speed, c = freq x wavelength

Phase difference = fraction of wavelength x 2pi

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Wave Properties


  • Straight waves directed at a certain angle to a surface will reflect off at the same angle
  • Angle between the reflected wavefront and wall and incident wavefront and wall are equal


  • When a wave changes speed when it crosses a boundary, its wavelength also changes
  • If wavefronts are at a non-zero angle to the boundary the direction of the wave will change as well


  • Diffraction occurs when waves spread out after passing through a gap
  • The narrower the gap the more the waves spread out
  • The longer the wavelength the more the waves spread out
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Wave Properties 2

The principle of superposition states that when two waves meet the total displacement at a point is equal to the sum of the individual displacements

  • Where a crest meets a crest reinforcement takes place and a supercrest if formed
  • When a crest meets a trough the resultant displacement is zero

Stationary Waves

  • When two people send waves along a rope from both ends the two sets of progressive combine to form a stationary wave
  • On a stationary there a points of zero displacement called nodes (where the waves cancel each other out) and maximum displacement called antinodes
  • At nodes the two waves are antiphase
  • When waves pass through each other at a constant frequency and phase difference, cancellation and reinforcement occur at fixed points. This is interference
  • Coherent sources produce an interference pattern due to the constant phase difference and frequency of the superimposing waves.
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Stationary wave test using microwaves

  •  Stationary waves are formed in air by the superposition of two waves
  • The stationary wave is formed in the region of the detector
  • These are the wave travelling towards the wall and its reflection from the wall 
  • minima and maxima are formed by destructive interference and constructive accordingly at points where the two waves are continuously in antiphase or in phase
  • The 2 waves have the same frequency and travel in opposite directions

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Stationary wave patterns

Stationary wave patterns are only produced at resonant frequencies. The is when an exact number of half-wavelengths fit into the string. Stationary waves don't transfer energy

  • The simplest wave pattern is produced at the fundamental frequency
  • There are nodes at either end of the wave and they have no amplitude
  • At a node there is destructive interference and at a antinode there is constructive interference
  • nth overtone = n+1th harmonic
  • At the ath harmonic, the number of antinodes = a, and the number of nodes = a+1
  • At the ath harmonic a/2 wavelengths fit into the string
  • If you are given the fundamental frequency, the resonant frequency of the ath harmonic = a x fundamental frequency
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Light shone through a narrow slit will sometimes produce a diffraction pattern.

  • The light source needs to be monochromatic (same wavelength) so that the waves diffract by the same amount resulting in a clear interference pattern
  • The pattern has a bright central fringe and alternating bright and dark fringes
  • Constructive interference has path difference n wavelengths, destructive interference has path difference (n+0.5) wavelengths

Double-slit interference

  • At a bright fringe the light wave from each slit arrive in phase with each other
  • At a dark fringe the light wave from each slit arrive antiphase (180 degrees out of phase) with each other
  • distance from central maxima to first order maxima is the fringe spacing, w
  • D is distance from the screen
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Diffraction 2

Diffraction is the spreading of waves as they pass through a gap

Diffraction of a single slit

  • Central fringe is produced and has the highest intensity
  • Central fringe is twice as wide as the outer fringes
  • Intensity of light decreasing further from the central fringe
  • Each outer fringe is of equal length
  • Greater wavenlength of light produces fringes that are further apart

Diffraction of double slits

  • Slits need to be close enough so that the light from each slit overlaps
  • Each slit must be narrow enough to allow for sufficient diffraction
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The double slits are coherent sources because the light emitted is of constant phase difference.

In the double slight experiment the fringe seperation depends on the colour of light used

  • White light consists of a continuous spectrum of colours: from with the range 650nm (red) - 350nm (blue)
  • Each colour of light has it own wavelength
  • Fringe seperation for red light is greater than that of blue light because the wavelength of red light is greater
  • The longer the wavelength, the greater the fringe seperation
  • Vapour lamps/discharge tubes produce light of a dominant colour
  • Light from a filament lamp covers a continuous spectrum therefore a filter is required to lower the range of wavelengths
  • Laser light is highly monochromatic. Double slits can be illuminated directly without the use of a single slit first

For white light:

  • central fring is always white
  • inner fringes are blue on the inner side and red on the outer
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Diffraction Grating

When monochromatic light is incident upon many close slits a giffraction grating is produced

  • Light from a diffraction grating only travels in certain directions
  • Light waves through adjacent slits reinforce each other in certain directions and cancel out in other directions
  • Central beam of a diffraction grating is the zero order beam, which goes in the same direction as the incident beam
  • Angle between zero order beams and following orders increases if light of a longer wavelength is used, grating with closer slits is used


  • d = dist. between gratings (m), smaller d = greater theta
  • theta = angle of diffraction
  • max no. of orders = d/wavelength (sin90=1)
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Closed and open pipe Harmonics


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