# The actual frequency of a wave that is the sum of sine waves with two different frequencies.

I am just trying to understand something.

Suppose you had two sine waves with two different frequencies, same amplitude and no phase difference.

Freq 1: 1 hz and Freq2: 2 hz and you added them together, how would you calculate the actual frequency of the resultant waves?

Is there a quick formula I can stick it into?

Thanks

Saying no phase difference does not make sense if the frequencies are different. If you have the first rising zero crossings together, then next one will not be. The result will not be a sine wave, so there will not be one frequency. The period will be the least common multiple of the to periods, assuming one exists. You can use the function sum identities to see that you have a product of two sine waves, one at the average of the two frequencies and one at half the difference. In your example you would have the product of a $$1.5 Hz$$ wave and a $$0.5 Hz$$ wave.
If the ratio of the two periods is rational, write it in lowest terms as $$a/b$$. the sum is periodic with period the least common multiple of $$a$$ and $$b$$. Whether you want to call the reciprocal of that period the frequency depends on the application. It won't be the frequency of a pure sine wave even if you began with those.