...on a string of circular cross section depends on the tension in the sting, T, the radius of the string, R, and its mass per volume, p.
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Mass/unit length ρ = p*πR²
v = √[T/ρ] = √[(m*a)/(m/L)] = √[L*a] = √[L*(L/t²)] = √[L²/t²] = L/t = v
v = √[T/ρ] = √[(m*a)/(m/L)] = √[L*a] = √[L*(L/t²)] = √[L²/t²] = L/t = v