# A wave speed in a piano string of linear density 5.0 g/m is 140 m/s. What is the tension in the string?

Question

A wave speed in a piano string of linear density 5.0 g/m is 140 m/s. What is the tension in the string?

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1 year 2021-09-03T16:56:36+00:00 1 Answers 12 views 0

The tension in the string is 98 newtons.

Explanation:

Since a mecanical wave is propagated throughout the material of the string under tension, which is calculated by using the following formula:

$$T = v^{2}\cdot \mu$$ (1)

Where:

$$T$$ – Tension in the string, in newtons.

$$v$$ – Wave speed, in meters per second.

$$\mu$$ – Linear density, in kilograms per second.

If we know that $$v = 140\,\frac{m}{s}$$ and $$\mu = 5\times 10^{-3}\,\frac{kg}{m}$$, then the tension in the string is:

$$T = v^{2}\cdot \mu$$

$$T = 98\,N$$

The tension in the string is 98 newtons.