Key Equations

Wave speed	$v = \frac{λ}{T} = λ f$
Linear mass density	$μ = \frac{mass of the string}{length of the string}$
Speed of a wave or pulse on a string under tension	$\| v \| = \sqrt{\frac{F_{T}}{μ}}$
Speed of a compression wave in a fluid	$v = \sqrt{\frac{Β}{ρ}}$
Resultant wave from superposition of two sinusoidal waves that are identical except for a phase shift	$y_{R} (x, t) = [2 A cos (\frac{ϕ}{2})] sin (k x - ω t + \frac{ϕ}{2})$
Wave number	$k \equiv \frac{2 π}{λ}$
Wave speed	$v = \frac{ω}{k}$
A periodic wave	$y (x, t) = A sin (k x \mp ω t + ϕ)$
Phase of a wave	$k x \mp ω t + ϕ$
The linear wave equation	$\frac{\partial^{2} y (x, t)}{\partial x^{2}} = \frac{1}{v_{w}^{2}} \frac{\partial^{2} y (x, t)}{\partial t^{2}}$
Power averaged over a wavelength	$P_{ave} = \frac{E_{λ}}{T} = \frac{1}{2} μ A^{2} ω^{2} \frac{λ}{T} = \frac{1}{2} μ A^{2} ω^{2} v$
Intensity	$I = \frac{P}{A}$
Intensity for a spherical wave	$I = \frac{P}{4 π r^{2}}$
Equation of a standing wave	$y (x, t) = [2 A sin (k x)] cos (ω t)$
Wavelength for symmetric boundary conditions	$λ_{n} = \frac{2}{n} L, n = 1, 2, 3, 4, 5 ...$
Frequency for symmetric boundary conditions	$f_{n} = n \frac{v}{2 L} = n f_{1}, n = 1, 2, 3, 4, 5 ...$