procedural wavy UV

[gentle sierra]

trying to make a laser.
is it possible to make what I drew in the picture procedurally? using wave math perhaps. (I am very bad with shaders atm)
I know I could draw a texture and be done with it but I think procedural visuals are cheaper. How can I make this happen?
Also this needs to scroll sideways by time * speed, so the wave goes up and down.

all I got is this:
UV.y + sin(UV.x * frequency + time * speed) * amplitude
and no idea how to implement.

PS. if anyone knows a good shader course that actually teaches instead of asking to repeat steps mindlessly, feel free to share.

[tepid dust]

Cheaper in terms of what? Looking at the way you generate the gradient, it might be cheaper to sample it as a texture before applying the formula you found.

The formula is pretty simple - just modify the uvs before using them.

As for courses, there are plenty online(just Google), but shaders are closely intertwined with computer graphics/rendering in general, so you should probably learn how rendering works(graphics pipeline on the GPU) first.

[gentle sierra]

I did something. But I feel like I better stick to drawing seamless textures instead of trying to be Stephen Hawking.