Question 6: What are the conditions for constructive and destructive interference?

ANSWER

Interference of two (or more) waves can be observed by seeing the waves reinforce one another at some points of the region or cancel one another at the other. So it can take place when

• Two waves have same frequency.
• They have the same wavelength.
• The principle of linear superposition is obeyed.
• The direction of propagation is the same.

So when they reinforce one another,the crest of one wave superpose with the crest of the other wave. Similarly,the trough of one wave overlaps with the trough of the other wave. On the other hand, when they cancel one another, the crest of one wave superpose with the trough of the other wave and vice versa.

Conditions for constructive interference

1. The two waves are in phase. The initial angle of the waves at the origin must be same. And if the wavelengths and frequencies are same, the waves would have no crossings of crests and troughs. (Remember when the angle is same, the waves are in phase).
2. Path difference is either zero or an integral multiple of the wavelength of either wave. In both cases a crest of one wave will meet a crest of the other and trough of one will meet the trough of the other as they propagate.
   Mathematically, path difference = d = 0, λ, 2λ, 3λ……….

Conditions for destructive interference

1. The two waves are anti-phase or out of phase.
2. The path difference of the two waves is half the wavelength or is odd multiple of half the wavelength. In both cases, trough of one wave will meet the crest of the other wave and vice versa.