Sum of 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. How do you add two signals with different frequencies?

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.

How do you add two signals with different frequencies?

You can go that in algebra: g(t) = f1(t) + f2(t). There you are, it is done. If you know what the signals are you can do it in time domain or in frequency domain. If they were more comoicared, then use Fourire too make them into sine waves and then combine them.