How Do You Add Angular Frequencies in Wave Simulations?

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SUMMARY

The discussion focuses on the process of adding angular frequencies in wave simulations, specifically for creating a simulation of beats. The user seeks to understand how to combine multiple angular frequencies (w1, w2, w3, etc.) to generate a resultant frequency (w1,2,3,...n) for plotting wave packets. The user emphasizes the need for clarity on this addition process, distinguishing it from calculating beat frequencies. The conversation highlights a gap in available resources regarding the addition of angular frequencies.

PREREQUISITES
  • Understanding of angular frequency (w) in wave mechanics
  • Familiarity with wave packet theory
  • Basic knowledge of sound wave amplitude displacement equations
  • Experience with simulation tools for wave modeling
NEXT STEPS
  • Research the mathematical principles of adding angular frequencies in wave theory
  • Explore wave packet formation and its implications in simulations
  • Learn about Fourier analysis for frequency decomposition
  • Investigate simulation software options for wave modeling, such as MATLAB or Python libraries
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Students and professionals in physics, audio engineering, and computational modeling who are involved in wave simulations and require a deeper understanding of angular frequency addition.

Ginny Mac
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I am working on creating a simulation of beats. I need to start with:

(where w is angular frequency),

w1 + w2 = w1,2
then
w1,2 + w3 = w1,2,3
then
w1,2,3 + w4 = w1,2,3,4
and so on, to create a wave packet where I will plot w1,2,3,4...n.

My problem is that I do not understand how to add the angular frequencies in order to arrive at the resultant frequencies! I have only found equations for amplitude displacement of the sound wave, nothing about adding angular frequencies. And I know that I am not supposed to find the beat frequency.

Any help pointing me in the right direction would be appreciated. Thank you!

Ginny
 
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I don't understand what you are trying to do. Can you elaborate?
 

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