# Mechanical Waves

Waves.  The wave speed $v=\lambda f$, $\lambda$ – the wavelength, $f$ – the frequency.

Wave functions and wave dynamics.  The displacement of individual particles in the medium
$y(x,t)=A\cos[\omega(\frac xv-t)]$ (or, more intuitively, $y(x,t)=A\cos[\omega(t-\frac xv)]$)
$y(x,t)=A\cos2\pi(\frac x\lambda-\frac tT)$
$y(x,t)=A\cos(kx-\omega t)$, where $k=\frac{2\pi}\lambda$ and $\omega=2\pi f=vk$
Wave function: $\frac{\partial^2y(x,t)}{\partial x^2}=\frac1{v^2}\frac{\partial^2y(x,t)}{\partial t^2}$