How to add two sine waves with different frequencies

You can't add two sines of different frequencies. This is a fundamental limit which much of math and physics takes advantage of. Its also the basis of the fourier transform. To put it simply, sines of different frequencies are orthogonal.

1. What happens when you add two sine waves of different frequency?
2. Can you add frequencies together?

What happens when you add two sine waves of different frequency?

When two sinusoids of different frequencies are added together the result is another sinusoid modulated by a sinusoid.

Can you add frequencies together?

One way to combine two frequencies is to simply add them. This is a linear operation, and will result in just the two frequencies in the combined signal.