So, standing waves inside this fixed rectangular boundary oscillate in time at certain resonant frequencies parameterized by the integers n and m. As they oscillate in time, they do not travel and their spatial variation is sinusoidal in both the x- and y-directions such that they satisfy the boundary conditions. The fundamental mode, and , has a single antinode in the middle of the rectangle. Varying n and m gives complicated but predictable two-dimensional patterns of nodes and antinodes inside the rectangle.
So, standing waves inside this fixed rectangular boundary oscillate in time at certain resonant frequencies parameterized by the integers n and m. As they oscillate in time, they do not travel and their spatial variation is sinusoidal in both the x.- and y-directions such that they satisfy the boundary conditions The fundamental mode, and  has a single antinode in the middle of the rectangle. Varying n and m gives complicated but predictable two-dimensional patterns of nodes and antinod,es inside the rectangle.