Superposition of waves

• Superposition of waves


  When two or more waves of the same type meet at a point and interfere with eachother

  
• What will the displacements of the oscillations be when two or more waves of the same type meet at a point and interfere with each other?

  The vector sum of the individual displacements of the waves

  
• What will happen when two waves in phase superpose?

  Constructive interference/superposition: The peaks and troughs increase in amplitude

  
• What will happen when two identical waves in anti-phase superpose?

  Destructive interference/superposition: The peaks and the troughs cancel each other out

  
• What must waves be in order to superpose?

  Of the same type e.g. sound cannot superpose with light
• When would two transverse waves of the same type not superpose?

  If the they were polarized at right angles
• If two identical loudspeakers are placed one meter apart in a large room with no furniture and are connected to the same signal generator, what will happen and why?

  An interference pattern will be created meaning if you walked accross the room in front of the speakers you would pass through alternating loud and quiet regions regularly spaced out. This happens because the sound waves have identical frequencies and are in phase so regions of constructive and destructive interference occur

  
• Phase difference/shift


  difference in phase angle between two oscillations with the same frequency

  
• Path Difference

  The difference in distance from 2 sources to a particular point
• When do positions of maximum amplitude occur? (in terms of path difference)

  When the path difference is an even number of half wavelengths i.e. zero or a whole number of wavelengths
• When do positions of minimum amplitude occur?

  When the path difference is an odd number of half wavelengths
• When waves are in anti-phase how many radians are they out of phase?

  
• Interference when in phase and out of phase

  
• Interference patterns only occur if:

  -The waves are the same type-The sources are coherent (they have the same wavelength and frequency and maintain a constant relationship)-The waves have similar amplitude at the point of superposition
• How can electrons have similar properties to waves?

  They can be diffracted
• When will electrons diffract?

  If they are fired at a high velocity at a material such as graphite crystal that has atomic separations similar to its wavelength
• Wavelength of electron

  h/mv (h is planks constant) orplanks constant/momentum
• What happens when a wave passes through a double slit?

  It is diffracted through each slit then because the diffracted waves are congruent where they meet superposition occurs - where crest meets a crest constructive interference- where crest meets a trough destructive interfenece

  
• Describe the path difference of a wave diffracted by two slits.

  There is a central maximum where there is 0 path difference and interference occurs then a 1st maximum either side of this where the path difference is λ then a second where it is 2λ and so on
• What formula can be used to link the path difference and the number of the maximum from the sensor?


  path difference = nλn is the order of the maximum from the centre

  
• Why is it difficult to observe interference effects with light?

  Because of the short wavelengths and the difficulty of providing coherent sources
• How did Thomas Young prove that light was a wave?

  From wave-fronts generated by passing single wavelength (monochromatic) light through a fine slit then using a double slit arrangement and observed the light and dark regions to prove interference had occurred
• interference fringes/young's fringes

  a pattern of light and dark bands on a screen, resulting from the constructive and destructive interference of light waves passing through two narrow, slowly spaced slits in a barrier
• Why are lasers often used to observe interference fringes?

  Because they have the same wavelength, are in phase and are polarized in the same pane
• How does a cd player work?

  Laser beams are shone onto the disc which has bumps of heigth of half a wavelength so when a beam is reflected off the top of a bump and another of the bottom of a dip they will be 1/2 a wavelength out of phase so will interfere constructively giving a binary 0. Otherwise the entire beam will be reflected giving a binary 1
• When are standing waves created?

  The superposition of two progressive waves of equal frequency and amplitude moving in opposite directions
• Differences between standing and progressive waves?


  Standing wave - Progressive wave Stores vibrational energy - Transmits vibrational energy Amplitude varies - Amplitude is constant All points between any two adjacent nodes are in phase - Phase varies smoothly with distance along the path of the wave Nodes are half a wavelength apart; antinodes are midway between nodes - No nodes or antinodes
• How can a standing wave be created between two speakers?

  If they are connected to the same signal generator and are facing eachother
• What will occur at the midpoint of two speakers connected to the same signal generator?

  The waves, having travelled the same distance at the same speed will always be in phase and interfere constructively.
• What happens a quarter of a wavelength either side of the midpoint of two speakers connected to the same signal generator?

  The distance from 1 speaker has increased by a quarter of a wavelength and the distance from the other has decreased by quarter a wavelength, this therefore means that the path difference is half a wavelength so the waves are in antiphase and destructive interference occurs
• What happens a half of a wavelength either side of the midpoint of two speakers connected to the same signal generator?

  The distance from 1 speaker has increased by a half of a wavelength and the distance from the other has decreased by half a wavelength, this therefore means that the path difference is wavelength so the waves are in phase and constructive interference occurs
• If you walked along a standing sound wave what would you hear?

  A series of equally spaced maxima and minima
• node


  point of zero amplitude in a standing wave

  
• point of zero amplitude in a standing wave

  node

  
• antinode


  point of maximum amplitude in a standing wave

  
• point of maximum amplitude in a standing wave

  antinode

  
• How big is the separation between adjacent nodes and antinodes


  Half a wavelength

  
• In what 3 ways do standing waves differ from travelling waves?

  -They store energy whereas travelling waves transfer energy-Their amplitude varies from zero at nodes to a maximum at antinodes but the amplitude of all the oscillations along a progressive wave is constant-Their oscillations are all in phase between nodes but the pase varies continuously along a travelling wave

  
• What happens when a pulse is sent along a rope that is fixed at one end?

  The reflected pulse is out of phase with the incident pulse

  
• Phase change


  When the phase of a wave is changed when it is reflected