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Sine Wave Beats

Sine Wave Beats
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2019-02-20 12:37
FunctionTrigonometryOptimizationSlider AnimationGraphing
This example demonstrates the phenomenon of sine wave beats. Key mathematical concepts include trigonometric functions, frequency distribution, and optimization problems. Construction involves GeoGebra commands such as a, δ, Φ, ω, f, g, etc. Suitable for high school or university mathematics courses to understand sine wave properties and optimization techniques.

GeoGebra Commands & Parameters

  1. Numeric a(2)
  2. Numeric δ(0.58)
  3. Numeric Φ(-2.3)
  4. Numeric ω(4.6)
  5. f(x) = (a * cos((ω * x))) + 5
  6. g(x) = (a * cos(((ω + δ) * x) + Φ)) + 5
  7. h(x) = f(x) + g(x) - 15
  8. p(x) = ((2 * a) * cos(((δ * x) + Φ) / 2)) - 5
  9. q(x) = ((2 * a) * cos(((δ * x) + Φ) / 2 + 3.141592653589793)) - 5
  10. Boolean Show(true)

AI Drawing Prompt Reference

Draw two sine waves with nearly the same frequency, one at 4.6 and the other at 5.18 (4.6+0.58), with an initial phase difference of -2.3. Add these two sine waves together to observe their interference pattern. Adjust parameters a, δ, and Φ to see how the waveforms change.
The prompt above was compiled from the original drawing commands and is for reference only.