Background: I'm writing a synthesizer with the creative limitation that it uses a single oscillator and a single amplitude multiplier.
$(t=$time, $f=$frequency, $a=$ amplitude$)$
What I'd like to do is cheat a bit and create something that approximates the sound of two sine waves using the above formula.
To put this mathematically,
What functions, $a$ and $f$, can I use in the above formula to get as close as possible to the following formula:
I don't believe that it's possible to find an exact way to emulate the second formula with the first but I'm assuming one could get pretty close.