Superposition Principle

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Two waves of the same frequency travelling in a medium arrive at a point exactly out of phase with equal amplitudes, so what is the resultant displacement there?

RankGuru · Accepted Answer

The principle of superposition in NCERT Class 11, Chapter 15 (Waves) states that when two waves overlap, the resultant displacement at any point is the algebraic sum of the individual displacements. If two waves of equal amplitude arrive exactly out of phase, meaning a phase difference of $\pi$ radians (half a cycle), their displacements are always equal and opposite. At every instant $y = A\sin(\omega t) + A\sin(\omega t + \pi) = A\sin(\omega t) - A\sin(\omega t) = 0$. This is complete destructive interference, giving zero resultant. The option of double amplitude describes constructive interference at zero phase difference, not $\pi$. The option equal to one amplitude would need a specific intermediate phase, not the fully opposed case. The option of $\sqrt{2}$ times the amplitude corresponds to a phase difference of $\pi/2$, not $\pi$. A consistency check: for equal-amplitude waves the resultant amplitude is $2A\cos(\phi/2)$; at $\phi = \pi$ this gives $2A\cos(\pi/2) = 0$, confirming exactly zero displacement.

Superposition Principle

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