1. Traveling Waves & Wave Equation
Sending a pulse down a string
T = tension µ = mass/length

2. Wave Equation: F =ma
For small angles:
Force
mass
accceleration

3. Wave Equation: Solutions
Any function y(x,t) will satisfy wave eq as long as x and t appear in the argument in the combination:

4. Sample Traveling Wave

5. Transverse traveling waves

6. Traveling Wave

7. Traveling Wave

8. Wave Equation Examples
Electric (E) or magnetic (B) field propagating in space from an oscillating charge (Light)
Current (I) or voltage (V) propagating in a coax cable
c - is the speed of light
The quantum-mechanical probability amplitude to find a particle at a certain location in space also satisfies a wave equation - Schroedinger’s Equation

9. Standing Waves Reflected pulse
But if we have a incident sinusoidal traveling wave and a reflected sinusoidal wave:

10. Standing Waves Trig

11. Standing Waves

12. Trig Review

13. Beats