Everyday, everywhere we go, we are surrounded by waves: the sounds we hear are carried through the air in waves; the heat we receive from the Sun arrives in waves; even the light reflected from this book travels toward your eyes in waves. It took scientists thousands of years to realize the importance of wave motion, and even longer to truly understand the behavior of waves. Today, a single equation is all that is needed to understand wave motion.

The first attempt to mathematically describe wave motion was made by Jean Le Rond d'Alembert in 1747. His equation sought to explain the motion of vibrating strings. While d'Alembert's equation was correct, it was overly simplistic. In 1749 the wave equation was improved upon by Leonhard Euler; he began to apply d'Alembert's theories to all wave forms, not just strings. For more than seventy years...