The wave equation describes the mathematical relationship between the spatial and temporal variations of a wave. It is commonly written as:
y = A sin(kx - ωt)
In this equation:
- y represents the displacement or amplitude of the wave at a given point in space (x) and time (t).
- A is the amplitude of the wave, which determines its maximum displacement.
- k is the wave number, which relates to the spatial frequency of the wave. It is equal to 2π divided by the wavelength (k = 2π/λ).
- x represents the spatial coordinate.
- ω is the angular frequency of the wave, which relates to its temporal frequency. It is equal to 2π multiplied by the frequency (ω = 2πf).
- t represents the time coordinate.
The equation represents a sinusoidal wave propagating in the positive x-direction. The term (kx - ωt) inside the sine function represents the phase of the wave at any given point in space and time. The wave equation describes how the amplitude of the wave varies as a function of position and time.