Some more pictures from MATH241
Plotting the normal modes of oscillation \phi(r,\theta)=J_n(z_{nm}r)Cos(n\theta), where J_n is the n^th Bessel function of first kind, and z_{nm} is its m^th zero.
Bessel function n=0, m=1
Bessel function n=0, m=2
Bessel function n=0, m=3
Bessel function n=1, m=1
Bessel function n=1, m=2
Bessel function n=1, m=3
Bessel function n=2, m=1
Bessel function n=2, m=2
Bessel function n=2, m=3
Bessel function n=3, m=1
Bessel function n=3, m=2
Bessel function n=3, m=3