Wave Equations

Moving string up and down

$$T=\frac{1}{f}=\frac{2\pi }{\omega }\cdots [\frac{\mathrm{s}}{\mathrm{cycle}}]$$ $$f=\frac{1}{T}=\frac{\omega }{2\pi }\cdots [\frac{\mathrm{cycle}}{\mathrm{s}}]$$ $$\omega =2\pi f=\frac{2\pi }{T}\cdots [\frac{\mathrm{rad}}{\mathrm{s}}]$$

Wave advances by one wavelength during each period. Wave speed is determined entirely by the mechanical properties of the medium in many situations and remains the same for all frequencies. If it doesn’t then the wave experiences dispersion.

$$\lambda =vT=\frac{v}{f}$$ $$v=\lambda f=\frac{\lambda }{T}$$