If you want accurate waves you might be better using either the Audio Waveform effect. Or, if you are feeling brave you can use expressions, using the Sin and Cosine functions, to generate whatever wave you like? Best to post in the Expressions forum if you prefer the latter?
I agree with Angie. This is a case of where you would ideally create a somewhat complex expression on a Write-On effect rigged with sliders and then by animating the sliders get different wave types and modulations. Even if you spend forever optimizing audio files or generating synthetic frequency modulations in Audition or another audio program, AE's audio infrastructure itself and in turn any effect relying on it are way too limited to correctly render those wave types.