Section 26.2
The Wave Equation
Describing how disturbances propagate through a medium without loss.
1
Introduction
The Wave Equation is a hyperbolic PDE:
is the wave speed. Note the second derivative in time (inertial/acceleration).
2
Based on F=ma
Forces on a string
Net vertical force on a segment is due to tension difference.
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Mass times acceleration equals force.
.
3
Worked Examples
Example 1: Traveling Waves
Verify works.
.
.
. Correct.
This is a right-moving wave.
Example 2: Standing Wave
Verify .
.
.
It works. This is a "Separation of Variables" solution.
Example 3: Visual Waves
The shape is preserved, just shifted to the right.
4
Practice Quiz
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