Two Ways to Derive the Wave Equation
Here are two different methods to derive the wave equation for a 1D wave on a string. The first method uses a finite difference and then the second method uses some magic math tricks.
Finally, I show a solution to the wave equation and animate it in python.
Here is the code to animate the wave.
https://trinket.io/glowscript/61b4850b73
Here is my finite difference calculation for a wave on a string
• The Wave Equation and Finite Differen...
The rest of the waves on strings playlist is here
• Waves on a String
00:00 - Intro
01:14 - Assumptions
02:30 - Finite Elements
04:40 - Calculating net force
08:11 - Net force equal to mass * acceleration
09:47 - Showing the second partial derivative
12:20 - The wave equation
14:15 - Differential method
16:57 - Net force
21:26 - The wave equation (again)
21:43 - Sample solution
24:50 - Plotting with python