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The mass density of platinum is 21.4 × 103 kg/m3. A platinum wire with a radius of 0.500 mm, 1.20 m long,
fixed at both ends has a frequency of vibration for its third harmonic equal to 512 Hz. What is the tension in the
wire?
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Answer #1

3λ/2 =l

 

v=fλ

v =2fl/3

v =√(T/μ)

given f = 512 Hz

√(T/μ) = 2fl/3

T = 4μf2l2/9

   μ =m/l =  (massdensity)A  = 21.4*103*π*0.5*0.5*10-6 = 16.8 x10-3 Kg/m

T = 16.8*10-3*4*512*512*1.2*1.2/9

  T=2819 N

 T =2.819 kN

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