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? A)4.00 kN B)2.00 kN C)2.82 kN D)1.41 kN E)1.00 kN

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Quizplus · Accepted Answer

The tension in the wire can be calculated using the formula for the frequency of the nth harmonic: $ f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}} $, where $ \mu $ is the linear mass density. First, calculate $ \mu $ using the volume and mass density: $ \mu = \rho \times \pi r^2 $. Then solve for tension $ T $ using the given frequency for the third harmonic (n=3).

The Mass Density of Platinum Is 21