The animation represents the mathematical description of a harmonic wave. Amplitude, wave number, and angular frequency are adjustable in real time.
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Description of the Animation
The animation visualizes a harmonic wave function, which describes a 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 Controls
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.
Overview
| Title | The Wave Function |
| Target Audience | Teachers and Lecturers |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Open Source – CC BY 4.0 |
| Attribution Notice | Created with AI assistance |