Generating a Plane with a big number of polygons?

I am currently working on a script, that makes a simple plane have waves and stuff,
But I currently have the problem, that I don’t want to make a mesh myself that has thousands of polygons just to cover a big area.

How could I generate A mesh like that?

You can do it in shaders, I believe that it would be a better place for you wave code as well. Shaders are scripts that run on the GPU.