Waves — Formula Sheet

y(x,t) = a \sin(kx - \omega t + \phi)

\lambda = \frac{2\pi}{k} \text{ or } k = \frac{2\pi}{\lambda}

\omega T = 2\pi \text{ or } \omega = \frac{2\pi}{T}

\nu = \frac{1}{T} = \frac{\omega}{2\pi}

\nu = \frac{\omega}{2\pi}

v = \frac{\omega}{k}

v = \sqrt{\frac{T}{\mu}}

\mu = \frac{m}{L}

v = \sqrt{\frac{B}{\rho}}

v = \sqrt{\frac{Y}{\rho}}

v = \sqrt{\frac{P}{\rho}}

The speed of a progressive wave is v = ω/k = λν = λ/T.

Positive x-direction wave

y = a sin(kx - ωt + φ).

The relations are λ=2π/k, ωT=2π, ν=1/T=ω/2π, and v=ων/k=λν=λ/T.