Interference of 2D waves

Cécile Geier PHYS 101LO8

Interference Constructive Destructive Sources

Content

Occurs when 2 waves, travelling in the same medium, meet

Here we will consider waves originating from 2 distinct sources

Interference

Constructive

Two travelling waves are in phase λ1= λ2

S1

S2

Equation Δd= d1-d2 = (n-m)λ = pλ RESULT: integer multiple of wavelenght Symbols:

n: # of wavelenghts between source 1 and point of interference

m: # of wavelenghts between source 2 and point of intererencep integer (0,±1, ±2, ±3,…)

The 2 waves must be in phase waves meet at their peak (may be maximum or minimum) There must be an integer number of

wavelenghts between the each source and the point of interference

Here: wave 1 has m=3 and wave 2 has n=2

Conditions

Destructive

Two waves are out of phaseλ1= ½ λ2

S1

S2

Equation Δd= d1-d2 = (n+ 1/2)λ Symbols:

n: # of wavelenghts between source 1 and point I

n is an integer (0,±1, ±2, ±3,…)

Wavelengths of both waves are shifted by ½λ

Both waves are not in phase When both waves meet one wave is at a

peak (maximum or minimum) and the other wave is at a lower point (not at the highest point)

Conditions