Chapter 13.10, Problem 16MP

Consider the normal modes of vibration for a square membrane of side $\pi$ (see Problem 6.3 ). Sketch the 2,1 and 1,2 modes. Show that the line $y=x$ is a nodal line for the combination $\sin x\sin 2y-\sin 2x\sin y$ of these two modes. Thus find a vibration frequency of a membrane in the shape of a ${45}^{°}$ right triangle.