Displacement Relation in a Progressive Wave: The displacement relation in a progressive wave describes the relationship between the displacement of the medium and the position of the wave. In a progressive wave, the disturbance or vibration in the medium creates a wave that travels through the medium.

The displacement relation shows that the displacement of the medium at any given point and time is determined by the wave’s amplitude, wavelength, frequency, and phase constant. As the wave travels through the medium, the displacement of the medium changes with time and position. The displacement relation is a fundamental concept in wave physics and is used to understand the behavior of many different types of waves, including electromagnetic waves, sound waves, and water waves.

Displacement Relation in a Progressive Wave

The displacement of the medium can be described by a sine or cosine function:

y(x, t) = A sin(kx – ωt + φ)

Where:

• y is the displacement of the medium at position x and time t
• A is the amplitude of the wave
• k is the wave number, which is related to the wavelength λ by k = 2π/λ
• ω is the angular frequency, which is related to the frequency f by ω = 2πf
• φ is the phase constant, which determines the starting point of the wave.

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By Team Learning Mantras