11.1.7. Worked Example

Try these first

1. 1.

   What is the standard form of the wave equation?

   Hint

   Remember the general representation of wave equations.

2. 2.

   Identify the boundary conditions in our example.

   Hint

   Think about the values of the function at the ends of the string.

3. 3.

   What does the wave equation model?

   • Particle Motion
   • Wave Propagation
   • Fluid Dynamics

   Hint

   Think about the contexts where waves are discussed.

4. 4.

   True or False: The initial displacement affects the shape of the wave.

   • True
   • False

   Hint

   Consider the importance of initial conditions.

5. 5.

   Consider a wave equation defined in a region with non-fixed boundary conditions. Describe how this would affect your solution approach.

   Hint

   Think about how the ends of a string can move.

6. 6.

   Using Fourier series, compute the solution for initial conditions that change over a range of values rather than fixed points.

   Hint

   Consider how you can represent varying functions in terms of sines and cosines.