When two or more than two waves travelling through a medium at the same time, the resultant displacement at any point is equal to the vector sum of their individual displacement caused by each wave separately at that point.
i.e., y = y1 + y2 +…… yn
y = resultant
yn = individual displacement
If the displacement are along the same direction we can write,
y = y1 + y2+ y3 + ……yn
If two waves each of same amplitude undergo superposition, the result displacement is:
y = a + a = 2a (Constructive interference)
y = a – a = 0 (Destructive interference)
This principle is used to explain different wave phenomenon such as interference, beats etc as:
- When two waves having same frequency are moving in a same direction superpose, constructive interference is produced.
- When two waves in the opposite direction superpose, stationary waves are formed.
- When two waves of slightly different frequencies are travelling in the same direction, beats are formed.