y(x, t)

y(x) = e^{−x^{2}}

y(x) = e^{−(x−3)^{2}}

y(x) = e^{−(x−6)^{2}}

y(x, t) = e^{−(x − 3 \frac{m}{s} t)^{2}}

y(x, t) = e^{−(x − vt)^{2}}

y(x, t) = Af(x) g(t) = A sin (\frac{nπx}{L}) cos(ωt)

k = \frac{nπ}{L}

k = \frac{2π}{λ}

y(x, t) = Af(x) g(t) = A sin (kx) cos(ωt)

y(x, t) = A sin (kx − ωt)

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

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

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

\frac{∂^{2}y}{∂x^{2}} = \frac{k^{2}}{ω^{2}} \frac{∂^{2}y}{∂t^{2}} = \frac{1}{v^{2}} \frac{∂^{2}y}{∂t^{2}}

v = \frac{ω}{k}

sin(α) cos(β) = \frac{1}{2}[sin(α + β) + sin(α − β)]

y(x, t) = A sin(kx) cos(ωt)

y(x, t) = \frac{A}{2} [sin(kx + ωt) + sin(kx − ωt)]

ω_{n} = \frac{nπ}{L} \sqrt{\frac{T}{μ}}

y(x, t) = \frac{A}{2} [sin (\frac{nπ}{L} x + \frac{nπ}{L} \sqrt{\frac{T}{μ}} t) + sin (\frac{nπ}{L} x − \frac{nπ}{L} \sqrt{\frac{T}{μ}} t)]

y(x, t) = \frac{A}{2} [sin \{\frac{nπ}{L} (x + \sqrt{\frac{T}{μ}} t)\} + sin \{\frac{nπ}{L} (x − \sqrt{\frac{T}{μ}} t)\}]

y(x, t) = y (x ± vt) = y (x ± \sqrt{\frac{T}{μ}} t)

v = \sqrt{\frac{T}{μ}}

y(x, t) = A sin (\frac{nπx}{L}) cos(ω_{n}t)

y(x, t) = \frac{A}{2} [sin (\frac{nπx}{L} + ω_{n}t) + sin (\frac{nπx}{L} − ω_{n}t)]