WAVE AND QUANTUM BEHAVIOUR

WAVE AND QUANTUM BEHAVIOUR

1. Superposition and Coherence

   • Superposition happens when two or more waves pass through each other.
     • At the instant the waves cross, the displacements due to each wave combine.
   • When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements.
   • CONSTRUCTIVE or DESTRUCTIVE interference
     • Contructive: crest + crust or trough + trough.
     • Total destructive interference: trough + crest (of equal size).
     • If the trough and crest aren't the same size, then the destructive interference isn't total - for the interference to be noticabe, the two amplitudes should be nearly equal.
   • You can use phasors to show superposition.
     • The phasor rotates anticlockwise through one whole turn as the wave completes a full cycle.
       • To find the resultant at time t, add the phasors tip to tail.
   • Being in phase means in step
     • Two points on a wave are in phase in they are both at the same point in the wave cycle.
     • Points that have a phase difference of 0 or a multiple of 360 are in phase - their phasors point in the same direction.
     • Points with a phase difference of odd number multiples of 180 (
   • To get interference patterns the two sources must be coherent
     • Two sources are coherent if they have the same wavelength and frequency and a fixed phase difference between them.
   • Constructive or destructive interference depends on path difference
     • Whether you get constructive or destructive interference at a point depends on how much further one wave has travelled than the other wave to get to that point (assuming the sources are coherent and in phase).
     • The amount by which the path travelled by one wave is longer than the path travelled by the other wave is called the path difference
     • Constructive interference - at any point an equal distance from both sources (that are coherent and in phase), or where the path difference is a whole number of wavelengths. Path difference = n
     • Total destructive interference - at any point where the path difference is an odd number of half wavelengths. Path difference = (n+1/2)

2. Standing Waves

   • You get a standing wave when a progressive wave is reflected at a boundary.
   • A STANDING WAVE IS THE SUPERPOSITION OF TWO PROGRESSIVE WAVES WITH THE SAME WAVELENGTH, MOVING IN OPPOSITE DIRECTIONS