Addition of two cosine waves with different periods

Question

I was just wondering if anyone knows how to add two different cosine equations together with different periods to form one equation. Is there a way to do this and get a real answer or is it just all funky math?

Also how can you tell the specific effect on one of the cosine equations that are added together.

Pretty please help

Thanks, Maddy :)

Answer 1

The sum of two cosine signals at frequencies $f_1$ and $f_2$ is given by:

$$ \cos( 2\pi f_1 t ) + \cos( 2\pi f_2 t ) = 2 \cos \left( \pi ( f_1 + f_2) t \right) \cos \left( \pi ( f_1 - f_2) t \right) $$

You may find this page helpful.