The traditional sine wave $\sin(x)$ is the sine wave that is wrapped around the function $f(x) = 0$. I.e., the $x$ axis. Is it possible to make an algorithm/formula/whatever so that you can take any function, e.g. $f(x) = x^2$ or $f(x) = tan(x)sec(x)$, and then produce a function that's either parametric or cartesian that represents the original $f(x)$ but with the sine wave along it.
For example, this question is a case where the sine wave is along a circle, and it's given in parametric form. But if for example it was along a parabola, or a line, a hyperbola, or an ellipse, or even just another $\sin(x)$, is there a general way to kind of "bend" the sine wave so that it would follow that curve?
Examples: $1/x$ would look like this: https://prnt.sc/jsji21
$x^2$ would look like this: https://prnt.sc/jsjg7o
Thanks in advance.