The solution to the standing wave equation for a stretched string is of the form
ψ(z,t)= Asin(kz)cos(ωt+φ)
and the total energy density of the standing wave is given by
W(z,t)= 1/2μ(∂ψ/∂t)²+1/2T(∂ψ/∂z)²
where T is the tension in the ring and μ is its linear mass density
(a) Show that the maximum kinetic density of an antimode on the string is given by 1/2μw²A².
(b) Show rhat the maximum potential energy of a node on the string is 1/2TK²A²