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# Suppose a harp string is tuned to middle C (C4) and is 0.81 m long...?

Suppose a harp string is tuned to middle C (C4) and is 0.81 m long. If I want the tension to be 200 N, what mass per unit length do I need? (Calculate your answer in kg/m)

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- JullyWumLv 79 years agoFavorite Answer
C4 frequency = 261.626 Hz

Assuming that a 0.81m string accommodates λ/2 when vibrating .. .. λ = 1.62 m

Wave velocity along the string, v = f x λ ..

v = 261.626Hz x 1.62 m .. .. v = 423.834 m/s

Equation for wave velocity .. v = √(T / μ) .. (μ = wire mass per m, kg/m) ..

μ = T / v² .. .. μ = 200 N / (423.834)² .. .. .. ►μ = 0.0011 kg/m

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