Chapter 12

• The principal of superposition of waves states that when two waves meet at a point in space, the resultant displacement is equal to the sum of the displacements of the individual waves
• Constructive interference is the superposition of two waves in phase creating a resultant displacement with a displacement greater than the individual displacements
• Destructive interference is the superposition of two waves out of phase resulting in a resultant displacement less than the individual displacements
• Coherence is when two waves with the same frequency have a constant phase difference
• An interference pattern is formed when two waves interact. It is made up of maxima, points of maximum displacement, and minima, points of minimum displacement
• Path difference is the difference in the distance travelled from two sources to a point.
• To investigate the wave nature of a light, Young's double-slit experiment is used. Monochromatic light is shone through a narrow single slit and then two narrow slits which creates two coherent sources of light. A Interference pattern is then formed on the screen behind the light showing the wave nature of light.
• $\lambda=$$\frac{ax}{D}$


  where a is the distance between slits

  D is the distance between the slits and screen

  X is the distance from maxima
• A stationary wave/ standing wave is a wave that remains in a constant position with no net transfer of energy and is characterised of nodes and anti-nodes
• Stationary waves are formed by the superposition of two progressive waves travelling in opposite directions which have the same frequency
• The distance between two adjacent points on a wave is $L=$$\frac{1}{2}\lambda$
• Progressive waves transfer energy in the direction of the wave
• Stationary waves have no net energy transfer
• For progressive waves, the wavelength is the minimum distance between two adjacent points oscillating in phase
• For stationary waves, the wavelength is twice the distance between adjacent nodes is equal to the wavelength of the progressive waves that created the stationary wave
• For stationary waves, between nodes the wave is in phase and on opposite sides of a node they are in antiphase
• For progressive waves, all parts of the wave have the same amplitude
• Fundamental frequency is effected by string mass, tension and length
• A stationary wave can be created on a taunt string. The string is plucked creating a progressive wavethe wave travels to the end and is reflectedthis creates two progressive waves travelling in opposing directionswhich forms a stationary wave
• Fundamental frequency is the minimum frequency of a wave for a string
• Harmonics for a stationary wave between the fixed ends of a string

  
• Harmonics of a stationary wave in a tube which is closed at one end

  
• Harmonics of stationary waves in an open ended tube.