Wave speed of a stretched string

Aaron7

1. The problem statement, all variables and given/known data
A rubber string when unstretched has length L₀ and mass per unit length μ₀. It is clamped by its ends and stretched by ΔL. The tension is T=κΔL / L₀.

Show that the wave speed on the rubber string when stretched by ΔL is

1/L₀ √( (κ/μ₀) ΔL(L₀+ΔL) )


2. Relevant equations
c = √(T/μ)
δ²y/δx² = 1/c² δ²y/δt²


3. The attempt at a solution

Using the formula c = √(T/μ) and putting in T I get:

c = √( κΔL/L₀μ₀ )

but I am not sure how to arrive at the answer or whether this is correct?

Many thanks.