The animation represents the mathematical description of a harmonic wave. The amplitude, wave number, and angular frequency can be adjusted interactively, causing the wave properties to update in real time.
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Description of the animation
The animation visualizes the wave equation, which describes a harmonic wave in space and time:
[ y(x,t) = A sin(kx – omega t) ]- A: Amplitude. The maximum displacement of the wave from its equilibrium position. A larger amplitude means a stronger oscillation.
- k: Wave number. It describes how many wavelengths fit into a given distance and is defined as k = 2π/λ, where λ is the wavelength.
- ω (omega): Angular frequency. It indicates how quickly the wave changes over time and is defined as ω = 2π/T, where T is the period.
- x: Spatial coordinate along the direction of wave propagation.
- t: Time. The term (kx – ωt) describes the propagation of the wave in the positive x-direction.
Interactive control
With the three sliders, you can directly adjust the wave parameters:
- Amplitude A: Changes the height of the wave. With a small amplitude, the wave oscillates weakly; with a large amplitude, it oscillates strongly.
- Wave number k: Determines the spatial frequency of the wave. A larger k-value results in more wave crests over the same distance (shorter wavelength).
- Angular frequency ω: Controls the speed of wave propagation. A higher angular frequency makes the wave oscillate faster.