Two steel wires are stretched with the same tension. The first wire has a diameter of 6.00E-4 m and the second wire has a diameter of 8.90E-4 m. If the speed of waves traveling along the first wire is 53.2 m/s, what is the speed of waves traveling along the second wire?
Wave velocity v = √(T/μ) Same tension in both wires: T1 = T2 μ is the linear mass density v1 = 53.2 m/s v2 = ? = v1/v2 = √(T1/μ1) / √(T2/μ2) = √(T1μ2 / T2μ1) = √(T1/T2 * μ2/μ1) = √(μ2/μ1) Linear mass density is mass/length, mass is density*volume: m/L = ρV/L = ρAL/L = ρA = ρπr^2 Both wires are steel so their density is the same. == v1/v2 = √(μ2/μ1) = √(ρπr2^2 / ρπr1^2) = √(r2^2 / r1^2) = r2/r1 == v2 = v1r1/r2 = (53.2*3.00×10^-4) / 4.45×10^-4 = 35.9 m/s ---- Speed of waves along the second wire is 35.9 m/s
