11.1.4. Boundary Conditions (BCs)

Try these first

1. 1.

   Define what a fixed end condition is and give an example.

   Hint

   Think of musical instruments for examples.

2. 2.

   What does Neumann BC signify?

   Hint

   Consider the forces acting on the ends.

3. 3.

   What does Dirichlet Boundary Condition specify?

   • Movement is allowed at ends
   • Endpoints are fixed
   • Wave must travel endlessly

   Hint

   Consider how the ends interact with waves.

4. 4.

   True or False: Free end conditions result in reflected waves.

   • True
   • False

   Hint

   Think about what happens at an end that isn't fixed.

5. 5.

   Consider a string fixed at both ends with a tension of 20 N and a mass of 2 kg. What is the wave speed on the string?

   Hint

   Find the mass per unit length!

6. 6.

   How do boundary conditions affect the frequencies of vibration in a fixed vs. free end scenario?

   Hint

   Think about harmonic series in both scenarios.