# What are the frequency bounds of waves from sine wave additive synthesis?

• hotwheelharry
In summary, when adding waves of a given frequency with the same phase, the resulting wave will have the same frequency. This is similar to adding complex numbers, where the phase factor is the only determining factor. The concept of frequency can be understood through the use of the Fourier transform, which is a linear operation. Therefore, adding two functions in the time domain results in adding their Fourier transforms in the frequency domain. This means that no new frequencies are created when adding waves. In the given scenario, starting with a frequency range of 100-200hz and adding waves will result in a final wave within the same frequency range.

#### hotwheelharry

Hello,

If I can make any number of waves (n) all with the same phase but all within a frequency range of 100-200hz, what are the ranges of frequencies I can make when adding them?

So would I be able to make a wave with frequency 400hz, or 25hz, using additive synthesis and these constraints? Then, if so, how do I calculate what the exact range I could make is?

Old frequencies do not beget new frequencies.

When you add waves of a given frequency, you only get waves of the same frequency. It's like adding complex numbers. It's just the phase factor that counts.

How do you make sense of frequency? Fourier transform. Fourier transform is linear. So, if you add two functions, you add the Fourier transforms to see what happens in the frequency domain. If some frequency component is zero for two functions, then it will be zero for their sum. Addition doesn't give you any new frequencies.

So if you start with a frequency range of 100-200hz, by adding things, you stay within 100-200hz.

Oh, you made it clear with the Fourier transform sections being 0. I knew you could make a square wave with infinity frequencies added but I guess the frequency of that saw is just the lowest frequency added in the sum. Thanks for the response.