Wave speed of a stretched string

  1. 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.
     
  2. jcsd
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