8	Good vibrations Wave Equation

What does it say?

The acceleration of a small segment of a violin string is proportional to the average displacement of neighbouring segments.

Why is that important?

It predicts that the string will move in waves, and it generalises naturally to other physical systems in which waves occur.

What did it lead to?

Big advances in our understanding of water waves, sound waves, light waves, elastic vibrations. . . Seismologists use modified versions of it to deduce the structure of the interior of the Earth from how it vibrates. Oil companies use similar methods to find oil. In Chapter 11 we will see how it predicted the existence of electromagnetic waves, leading to radio, television, radar, and modern communications.