y(x, t) = A cos(kx − ωt)

\frac{∂^{2}y}{∂x^{2}} = −k^{2} A cos(kx − ωt)

\frac{∂^{2}y}{∂t^{2}} = −ω^{2} A cos(kx − ωt)

k^{2} A cos(kx − ωt) = (\frac{k^{2}}{ω^{2}} ) ω^{2} A cos(kx − ωt)

\frac{k}{ω} = \frac{2π/λ}{2πf} = \frac{1}{fλ}

\frac{∂^{2}y}{∂x^{2}} = \frac{1}{V^{2}} \frac{∂^{2}y}{∂t^{2}}

\frac{∂^{2}E}{∂x^{2}} = \frac{1}{c^{2}} \frac{∂^{2}E}{∂t^{2}}

∇^{2}E = \frac{1}{c^{2}} \frac{∂^{2}E}{∂t^{2}}

\begin{aligned}y_{1}(x, t) & = A_{1} cos(k_{1}x − ω_{1}t + ϕ_{1}) \\ y_{2}(x, t) & = A_{2} cos(k_{2}x − ω_{2}t + ϕ_{2}) \end{aligned}

\begin{aligned}y_{1}(x, t) & = A sin(kx − ωt) \\ y_{2}(x, t) & = A sin(kx − ωt + ϕ) \end{aligned}

sin(α) + sin(β) = 2 cos(\frac{α − β}{2} ) sin(\frac{α + β}{2} )

y1 + y2 = 2A cos(\frac{ϕ}{2}) sin(kx − ωt + \frac{ϕ}{2})

\begin{aligned}y_{1}(x, t) & = A sin(kx − ωt) \\ y_{2}(x, t) & = A sin(kx + ωt) \end{aligned}