Wave Speed on Stretched String – Rankers Physics
Topic: Waves
Subtopic: Standing Wave in String and Organ Pipe

Wave Speed on Stretched String

A stretched string of length \(1\text{ m}\) fixed at both ends having a mass of \(10^{-4}\text{ kg}\) is under a tension of \(16\text{ N}\). The speed of the transverse wave on the string would be
\(400\text{ m/s}\)
\(200\text{ m/s}\)
\(200\sqrt{2}\text{ m/s}\)
\(250\text{ m/s}\)

Solution:

Wave speed on a string is \(v = \sqrt{\frac{T}{\mu}}\), where \(\mu = \frac{M}{L} = \frac{10^{-4}\text{ kg}}{1\text{ m}} = 10^{-4}\text{ kg/m}\). Substituting the values, \(v = \sqrt{\frac{16}{10^{-4}}} = \sqrt{16 \times 10^4} = 400\text{ m/s}\).

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