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A platinum wire that is 1.20 M long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrat...

A platinum wire that is 1.20 M long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 x 10^3 kg/m^3. What is the tension in the wire?

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Answer #2

m = pi*r^2*L*rho = 3.14*0.5^2*10^-6*1.2*21.4*10^3 = 0.0202 kg

f3 = (3/2*L)*sqrt(T*L/m)

T = (f3*2*L/3)^2*m/L

T = (512*2*1.2/3)^2*0.0202 / 1.2 = 2824 N

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