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Aaron7 Apr4-12 11:29 AM

Wave speed of a stretched string
 
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.


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