The density of aluminum is 2700 kg/m³. If transverse waves travel at $38 \mathrm {~m} / \mathrm { s }$ in an aluminum wire of diameter $4.6 \mathrm {~mm}$ what is the tension on the wire?

Question

Quizplus · Accepted Answer

The tension $ T $ in the wire can be calculated using the formula for the speed of transverse waves: $ v = \sqrt{\frac{T}{\mu}} $, where $ \mu $ is the linear mass density. First, calculate $ \mu $ using the volume and density of aluminum: $ \mu = \text{density} \times \text{cross-sectional area} $. The cross-sectional area $ A = \pi \times (0.0023 \, \text{m})^2 $. Then solve for $ T $ using $ T = \mu \times v^2 $. The correct tension is approximately 65 N.

The Density of Aluminum Is 2700 Kg/m3 38 m/s38 \mathrm {~m} / \mathrm { s }38 m/s

The Density of Aluminum Is 2700 Kg/m³ $38 \mathrm {~m} / \mathrm { s }$