I know that $ \sin(x), \cos(x), \csc(x)\text{(cosec(x), I think)}, \sec(x)$ and such functions are capable of generating waves. Also, $\varphi(x)\sin(x)$ or $\varphi(x)cos(x)$ and such functions (where $\varphi(x) = \frac{1}{1+e^{-x}}$) can generate waves of increasing amplitude. What I want to know is : are there functions that can produces waves that resemble some sounds (like the sound that comes when someone says 'Hello') or those that sound like musical instruments (especially a square lead) ?
NB : I am asking this question just to know things. I had to post this question right after an exam and currently I am writing another exam, so forgive me for not searching the net for this). Also, please correct the tags.