A steel wire in a piano has a length of 0.5000 m and a mass of 3.800 10-3 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical scale)?

Answer 1

λ =2L=2•0.5 = 1 m
v= λ•f=1•261.6 = 261.6 m/s
v = sqrt(T/m₀)=
=sqrt(T•L/m)
v²= T•L/m
T= v²m/L=261.6²•3.8•10⁻³/0.5=520.10 N