Assignment:
Q1. Find the solution to the two-dimensional wave equation
Q2. Solve the two-dimensional wave equation for a quarter-circular membrane,
The boundary condition is such that u=0 on the entire boundary.
Q3. Consider Laplace's equation
a. Give a brief physical interpretation of this equation.
b. Suppose that u(x,y,t)=f(x)g(y)h(t)
What ordinary differential equations are satisfied by f, g, and h?
Provide complete and step by step solution for the question and show calculations and use formulas.