|Interference is said to occur when waves from two or more coherent sources superpose with one another producing a resultant wave.
Interference of water waves can be demonstrated using a ripple tank with two vibrating rod dippers. (see Figures below) The two dippers send our circular waves that are in phase and of the same frequency. An interference pattern consisting of easily observed lines of constructive(maxima) and destructive interference(minima) is seen.
The lines of constructive interference (maxima) are places where the resultant amplitude is double the amplitude of one wave. The lines of destructive interference (minima) are places where the waves cancel out and the resultant amplitude is zero.
a. Constructive Interference
Let the two sources (dippers) be S1 and S2 respectively. Assume that the two sources generate waves in phase.
For constructive interference to occur at a point P, the two waves must arrive in phase at P. This means that the wave crest from one source always meet the wave crest of the other. This can only occur if the path difference of the waves from the two sources is zero or they differ by an integral multiple of wavelength, i.e. nλ.
The condition for constructive interference is
Path difference S2 P – S1 P = nλ where n = 0,1,2,3…..is the order of the maxima.
b. Destructive Interference
Destructive interference occurs if the waves from the two sources arrive exactly out of phase at point P, i.e. the wave crest always meets the trough. This happens when the path difference of the waves is (n – ½)λ.
The condition for destructive interference is
Path difference S2 P – S1 P = (n-½)λ where n = 1,2,3…..is the order of the minima.
The Figure below illustrates the production of an interference pattern by two sources.
(a) Constructive interference occurs at P when the waves meet in phase because their path difference is xero.
(b) Constructive interference also occurs at Q because the path difference is 1 wavelength.
(c) Destructive interference occurs at R because the path difference is half a wavelength,
In general, for two sources which generate waves in phase, the conditions for
|1. Constructive Interference: Path Difference of the 2 waves = nλ
2. Destructive Interference: Path Difference of the 2 waves = (n – ½)λ
Chapter 3: Interference
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