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Addition of Sine Waves

Addition of Sine Waves
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2015-05-25 11:29
FunctionTrigonometrySlider Animation
This example demonstrates the addition of two sine waves. The core mathematical concepts involved are trigonometric functions. Using GeoGebra commands, two sine waves can be constructed and their sum can be observed by adjusting parameters. Suitable for high school mathematics education or students learning about the addition of sine functions.

GeoGebra Commands & Parameters

  1. Numeric a_1(2.0)
  2. Numeric a_2(2.0)
  3. Angle ϕ_1(0.0)
  4. Angle ϕ_2(1.0471975511965976)
  5. Numeric ω_1(5.0)
  6. Numeric ω_2(5.0)
  7. y_1(x) = (a_1 * sin((ω_1 * x) + ϕ_1))
  8. y_2(x) = (a_2 * sin((ω_2 * x) + ϕ_2))
  9. f(x) = y_1(x) + y_2(x)
  10. Boolean a(false)
  11. (a * false)
  12. (a * false)
  13. (a * false)

AI Drawing Prompt Reference

Draw two sine waves with the same amplitude and angular frequency but different phases, and display their sum. Use a slider to adjust the phase difference between the two sine waves and observe how the叠加 waveform changes with the phase difference.
The prompt above was compiled from the original drawing commands and is for reference only.