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

Two sinusoidal plane waves of the same frequency having intensities $I_{e}$ and $4 I_{e}$ are travelling in the same direction. The resultant intensity at a point at which waves meet with a phase difference of zero radian is
(a) $I_{\text {o }}$
(b) $5 I$
(c) $9 I$
(d) $3 I_{o}$

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Key Concepts

Phase Difference in Wave Superposition

The phase difference between waves determines how their peaks and troughs align. A phase difference of zero signifies that the waves are completely in phase, leading to maximum constructive interference, where the amplitudes add directly to produce a wave of higher amplitude and, consequently, greater intensity.

Wave Interference

Wave interference refers to the phenomenon where two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude. When waves are coherent—that is, they have a constant phase difference—their amplitudes add constructively or destructively, affecting the overall intensity of the resulting wave.

Amplitude-Intensity Relationship

In wave physics, the intensity of a wave is directly proportional to the square of its amplitude. This means that when combining waves, the resultant intensity depends on the square of the sum of their individual amplitudes, rather than the sum of their individual intensities.

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