Any ideas/ready-made solutions for rendering sound waves in the game?

Question

Programming

I want to implement sound waves in the game when the main character jumps. Waves like those that remain on the water when a stone is thrown into it. But I don't even know how to approach this issue. The problem is that they (waves) must have the physics of collision with surfaces and reflection from them.
I'm using SpriteKit

Answer 1

Something like Dark Echo ?

Answer 2

Frank Luna's DirectX book describes water waves. A horizontal mesh is made (triangles). In the right places - indignation (height rise). Further in time, the height of the point is averaged from the neighbors. I am writing from memory (in order for the wave to go down, it is probably still necessary to take into account gravity). To dampen the waves, we add friction. In short, the formula reflects the numerical solution of dif. equations.