How Do You Add Angular Frequencies in Wave Simulations?

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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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