Superposition

• Principle of superposition


  When 2 waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point
• When two waves meet

  • If their displacement is in the same direction, they superpose (combine) to make a bigger displacement (constructive interference)
  • If a wave with positive displacement meets a wave with negative displacement, they will cancel out (destructive interference)
• Pulses heading towards one another


  • Pulses intersect
  • Pulses passed through one another
• Stationary wave


  • Formed when 2 progressive waves with the same frequency (similar amplitude) moving in opposite direction pass through one another and superpose
  • Only formed at harmonic (aka resonant) frequencies
• Node


  Point of minimum amplitude
• Antinode


  Point of maximum amplitude (midway between nodes)
• The distance between adjacent nodes is half a wavelength
• The lowest (longest) frequency of a possible stationary wave formed is the first harmonic (or fundamental frequency, f)
• For a string fixed at either end there are two nodes at the ends
• Tension, wave speed and the frequency of the first harmonic for a string under tension


  • You can tune a guitar by tightening the string (increase T, f increase)
  • You get a lower note by using a more massive string (μ increases, f decreases)
• We can show c = √(T/μ) = fλ
• The frequency of the nth harmonic is nf1, where f1 is the fundamental frequency
• The wavelength of the nth harmonic is L/n, where L is the length of the string
• The wave speed is the same for all harmonics
• The amplitude of the harmonics decreases as the harmonic number increases