Standing waves are produced by the superposition of two...

Standing waves are produced by the superposition of two waves $y_{1}=0.05 \sin (3 \pi t-2 x)$ and $y_{2}=0.05 \sin (3 \pi t+2 x)$ where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds. The distance (in meters) between two consecutive nodes is (A) $\pi / 2$ (B) $\pi$ (C) $0.5$ (D) $1.0$

Standing waves are produced by the superposition of two waves $y_{1}=0.05 \sin (3 \pi t-2 x)$ and $y_{2}=0.05 \sin (3 \pi t+2 x)$
where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds.
The distance (in meters) between two consecutive nodes is
(A) $\pi / 2$
(B) $\pi$
(C) $0.5$
(D) $1.0$

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Key Concepts

Standing Waves

Standing waves are a type of wave pattern that results from the interference of two waves with the same frequency and amplitude traveling in opposite directions. They are characterized by nodes and antinodes, where nodes are points that remain stationary, and antinodes are points where the oscillation amplitude reaches its maximum.

Superposition Principle

The superposition principle states that when two or more waves overlap in space, the resulting displacement at any point is equal to the sum of the displacements of the individual waves at that point. This principle is essential for understanding how standing waves are formed by the interference of two traveling waves.

Nodes

Nodes are specific points along a standing wave where the waveform always has zero amplitude, due to the destructive interference of the two opposing waves. The distance between consecutive nodes is related to the wavelength of the individual waves, typically being a fraction of the wavelength.

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