In short: Purple doesn’t have it’s own wavelength. Neither does white, black and the entire gray-scale or any mixing of any colour with the gray-scale and probably more. They’re called non spectral colours.

It might be easier to understand when considering other types of waves. At least it is for me. A simple sound can also be described as a wave with a frequency, but if we play two sounds at the same time, we can’t say that the sum of the waves has any specific frequency. The frequencies don’t add up or multiply or mix as average. The combined sound can only be described as the addition of two frequencies.

In musical terms, purple is not a note, but instead a chord or interval. Red and blue can be individual notes, or they can be mixed as intervals. White is noise and black is silence.