Two sinusoidal plane waves of the same frequency having...

Two sinusoidal plane waves of the same frequency having intensities $I_{0}$ and $4 I_{0}$ are traveling in the same direction. The resultant intensity at a point at which waves meet with a phase difference of zero radian is
(A) $I_{0}$
(B) $5 I_{0}$
(C) $9 I_{0}$
(D) $3 I_{0}$

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Key Concepts

Superposition Principle

This principle states that when two or more waves overlap in space, the resultant wave is the algebraic sum of the amplitudes of the individual waves. It is a fundamental concept in wave mechanics and interference, applicable to both constructive and destructive scenarios.

Constructive Interference

Constructive interference occurs when waves meet in phase, meaning their peaks and troughs align, resulting in a combined amplitude that is the sum of the individual amplitudes. This phenomenon leads to an increase in the resultant intensity, as intensity is proportional to the square of the amplitude.

Amplitude-Intensity Relationship

In wave physics, the intensity of a wave is proportional to the square of its amplitude. Therefore, when adding amplitudes from interfering waves, the resulting intensity is found by squaring the sum of the amplitudes, not by simply adding the individual intensities.

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