wave equation

A useful solution to the wave equation for an ideal string is:

 y(x,t) = Asin(2π/λ(x+/-vt))

This is a solution to the one-dimensional wave equation (via direct substitution):


∂ ² / ∂x² = (ρ/T)(∂²y/∂t²)

giving us:

1 =  (ρ/T)v²

giving the wave velocity of a stretched string:
v = √(T/ρ)
where T = tension in the string

and the mass her unit length:
ρ = m/L