Speed of Transverse Waves on a Steel Wire – Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

A steel wire \(0.50\text{ m}\) long has a mass of \(4.0 \times 10^{-3}\text{ kg}\). If the wire is under a tension of \(80\text{ N}\), the speed of transverse waves on the wire is
\[93 m s^{-1}\]
\[100 m s^{-1}\]
\[50 m s^{-1}\]
\[98 m s^{-1}\]

Solution Explained:

To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

Linear mass density \(\mu = \frac{m}{L} = \frac{4.0 \times 10^{-3}}{0.50} = 8.0 \times 10^{-3}\text{ kg/m}\). Wave speed is \(v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80}{8.0 times 10^{-3}}} = 100\text{ m/s}\).

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