asymmetrical sine wave

Question

How do you model a sine wave that begins to shift over asymmetrically (like a ocean swell approaching a beach)? Is sine even the right function for this model, or is some other type of function better?

Answer 1

Perhaps you could try something like

$$f(x) = - (1 + e^{-cx}) \arctan \left( \frac{\sin(x)}{1 + e^{-cx} - \cos(x)} \right) $$

where $c > 0$.

Answer 2

It's hard to tell exactly what you're asking, but you can try something like $ \frac{10}{\sqrt{x}}\sin(2\pi x)$, which starts with high amplitude then decreases. Or you could do the same thing with frequency, with $ \sin(2\pi \frac{10}{\sqrt{x}})$, which starts with a high frequency then slows down.