Recently, I stepped into the field of frequencies. There is a term "Mixer", that is dedicated to "mix" frequencies/audio signals together.

Following this thread I have a question:

**Why do we need a mixer, if in term of math we can simply add frequencies?**

*I bring the following materials to the table.*

I know that any sound has a harmonics. Harmonics I understand as a frequency on top (or below) given base frequency (I'll disregard amplitude and phase shift). So, in my head, we can get resulting frequency by adding two, like:

\( f_{a}+f_{b}=f_{c} \)

But mixers, as said, is a way to "multiply" frequencies/audio signals.

So, if I pluck an imaginary ideal string (disregarding the length) in an ideal imaginary space with no reflections, I should read an input as in the formula above, shouldn't I?

This is the screenshot I made, showing mixing formula found in the mentioned thread, and addition formula.

I would be a very thankful for the replay, explaining to me, what is the difference, or an error in my thoughts.

Thank you!