Two identical traveling waves, moving in the same direction,...

Two identical traveling waves, moving in the same direction, are out of phase by $\pi / 2$ rad. What is the amplitude of the
resultant wave in terms of the common amplitude $y_{m}$ of the two
combining waves?

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Key Concepts

Superposition Principle

The superposition principle states that when two or more waves traverse the same medium at the same time, the net displacement is equal to the sum of the individual displacements. This is fundamental for understanding how waves combine to produce a resultant wave.

Wave Interference

Wave interference occurs when two or more waves overlap, resulting in a new wave pattern. Depending on their phase relationship, the interference can be constructive (amplitudes add) or destructive (amplitudes subtract), which directly affects the resultant amplitude.

Phase Difference

The phase difference refers to the relative offset between the cycles of two waves. It is critical in determining the nature of interference; even a small phase difference can lead to significant changes in the resultant amplitude when waves interact.

Phasor Addition and Trigonometric Identities

Phasor addition is a technique that represents waves as vectors in the complex plane, simplifying the process of adding waves with different phases. This approach, combined with trigonometric identities, helps derive the amplitude of the resultant wave from the component waves.

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