Q.Two sound waves of equal amplitude $3\ \text{cm}$ and the same frequency arrive at a point with a constant phase difference of $60^\circ$. Find the amplitude of the resultant wave at that point.

When multiple waves overlap, the net displacement at any point is simply the sum of the displacements each wave would cause on its own.

Principle of Superposition: When two or more waves travel simultaneously through the same medium and overlap at a point, the resultant displacement of the particle at that point at any instant is the algebraic (vector) sum of the displacements due to each individual wave, as if the other waves were absent.

Mathematically, if y1, y2, ..., yn are the displacements that would be produced by waves 1, 2, ..., n acting alone, the resultant displacement is:

y = y1 + y2 + ... + yn

Each wave continues to travel through the medium independently, unaffected by the presence of the other waves, after they cross/overlap.

This principle explains phenomena such as interference (constructive and destructive), beats, and the formation of stationary (standing) waves.

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Principle of superposition: the resultant displacement due to several overlapping waves is the (vector) sum of the individual displacements each wave would cause on its own.

When two or more waves travel through the same region of a medium simultaneously, they overlap and interact. The principle of superposition states that the resultant displacement of any particle of the medium at any instant is equal to the vector sum (algebraic sum, for waves along the same line) of the displacements that would have been produced by each wave separately, as if the others were absent:

y(resultant) = y1 + y2 + y3 + ...

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