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A guitar has a steel string with a mass of 4.5 g in each metre, under a tension of 72 N…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A guitar has a steel string with a mass of $4.5\ \text{g}$ in each metre, under a tension of $72\ \text{N}$ . It also has a nylon string with $1.2\ \text{g}$ in each metre, under a tension of $60\ \text{N}$ . On which string do waves travel faster, and by how many times?

Need a reminder? The key ideaShow

On a string, $v = \sqrt{\dfrac{T}{\mu}}$ , with $T$ the tension and $\mu$ the mass of each metre. In a fluid, $v = \sqrt{\dfrac{B}{\rho}}$ ; along a solid rod, $v = \sqrt{\dfrac{Y}{\rho}}$ . In a gas (Laplace), $v = \sqrt{\dfrac{\gamma p}{\rho}} = \sqrt{\dfrac{\gamma R T}{M}}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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