Two sinusoidal waves with equal wavelengths travel along a...

Two sinusoidal waves with equal wavelengths travel along a string in opposite directions at $3.0 \mathrm{m} / \mathrm{s}$. The time between two successive instants when the antinodes are at maximum height is $0.25 \mathrm{s} .$ What is the wavelength?

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Key Concepts

Standing Waves

A standing wave forms when two waves of the same frequency and amplitude travel in opposite directions and interfere. The result is a wave pattern with fixed nodes (points of zero amplitude) and antinodes (points of maximum amplitude). This concept is essential for understanding how the interference of sinusoidal waves produces stationary patterns on a medium.

Relationship Between Wave Speed, Frequency, and Wavelength

In all wave phenomena, there is a fundamental relationship given by the equation v = f × ?, where v is the speed of the wave, f is its frequency, and ? (lambda) is its wavelength. This relationship allows one to compute one of these quantities when the other two are known, and is key to analyzing any wave motion.

Temporal Periodicity in Standing Waves

The oscillation at an antinode in a standing wave exhibits temporal periodicity, meaning that the displacement at that point varies sinusoidally with time. The period of oscillation (T) is the time taken for one complete cycle of motion. When two successive instances of maximum displacement occur at an antinode, their time difference corresponds to the period of the oscillation, which can then be used to determine the wave frequency.

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