In this worksheet we consider some examples of the vibrating patterns of rectangular membranes. Such membranes are described by the 2-dimensional wave equation diff(u(x,y,t),t,t) = c^2*Delta(u(x,y,t)) . we are mainly interested in the product solution obtained by the method of separation of variables, such product solutions of the wave equations are also called standing waves . In particular, we consider intricate patterns of nodal curves appearing when there is more than one eigenfunction corresponding to the same eigenvalue (this happens, for example, for a square membrane.