Here are two generic strings, one with Dirichlet boundary conditions, the other with Neumann boundary conditions: The left animation is a string with its ends held at fixed points; such a string is a Dirichlet string. The right animation, a Neumann string, has endpoints that can move freely, but the slope of the string at these points is fixed (note that the ends of the Neumann string are always perpendicular to the bounding lines).