When immersed in a high-frequency sound, the rim of a wine glass oscillates as shown in the picture below. If the sound has equal intensity in all directions from the center of the rim, then where are the nodes of the stationary waves (in the rim)? By symmetry, every point on the rim is the same, subject to the same environmental conditions. Then there is no reason why one particular point is the node while another point isn't. By symmetry, I conclude that either all points on the rim are nodes or all points are not. Then, it's impossible to have a stationary wave. How can this contradiction be resolved?