How to build a cylindrical wave model?

Question

Mathematics

Explain, please, the formula of a cylindrical wave . Actually, I want to build a WebGL model of a cylindrical wave, as in the pictures on Wikipedia, but I don’t know how to apply this formula to the Cartesian coordinate system.

Answer 1

If an approximate model is enough, you can do this:
r1=sqrt(x^2+y^2)
a=A*p/sqrt(p^2+x^2+y^2)
z=a*sin(k*r1 -w*t)
where p is the size of the area in the vicinity of zero with a forcibly limited amplitude,
A is the maximum amplitude (at zero)
k is the spatial frequency (i.e. 2*pi/k is the distance between the waves)
w is the temporal frequency ( 2*pi/w - period).
w/k is the speed of propagation.