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Mathematics

The Wave Equation and d'Alembert's Formula for Solutions

Quick fact

In 1746, Jean le Rond d'Alembert discovered that the solution to the one-dimensional wave equation is simply the sum of two arbitrary functions—one moving left and the other moving right—each preserving its initial shape perfectly.

Why this is interesting

If you pluck a guitar string, the bump splits into two waves that run away from each other. Could you predict exactly what the string looks like at any later time?