(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Describe the sum of two EM waves that have the same initial phase and same amplitude but different frequencies such that [tex]\omega _1 >> \omega _2[/tex].

2. Relevant equations

[tex]E=E_0 \cos (kx -\omega t + \alpha)[/tex].

3. The attempt at a solution

I summed them up and reached, after an approximation, that [tex]E_1+E_2 \approx 2 E_0 \cos \left (kx -\frac{\omega _1t}{2} + \alpha \right ) \cos \left ( \frac{\omega _ 1 t}{2} \right )[/tex]. I don't know how to simplify further. It seems that the amplitude is the sum of both amplitudes and I'm not sure yet what is the frequency. It should be almost [tex]\omega _1[/tex], intuitively. I just don't know how to show it.

Any help is appreciated.

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# Wave addition

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