1. Continuous String Take limit of h→0 and m/h→ r Wave Equation

2. Solutions to Wave Equation Traveling Wave Solution: Standing Wave Solution:

3. Normal Modes of Wave on String n= normal mode Can be broken down into a wave traveling + and one traveling –

4. Initial Conditions - Stationary If string with fixed endpoints is stationary at t=0 :

5. Other Boundary Conditions Slipping ring Other combinations

6. Traveling Waves

7. Traveling Waves (continued)

8. Reflections Wave functions must satisfy wave equation and boundary condition at end of rope

9. Wave Equation for Other Variables “Conjugate” variables Other wave equations

10. Power Transmission

11. Wave Equations for Other Systems E&M: Sound:

12. Wave Equation in 3 Dimensions E&M in free space: