Galileo and Hooke demonstrated that every sound is characterized by a precise number of vibrations per second, but the full understanding of even the simplest... vibrators requires... calculus. ...Leonard Euler, Daniel Bernoulli, Jean le Rond d'Alembert, and Joseph Louis Lagrange all studied the vibrating string.... In 1747 d'Alembert found... the wave equation and in 1753 Bernoulli stated the... decomposition of every motion of a string as a sum of elementary sinusoidal motions. Then at the beginning of the following century Fourier developed "harmonic analysis."