Question

The D string of a guitar is stretched to a tension of 150 N. The string has a mass of 3.4 g and is stretched to a length of 0.69 m. What is the speed of waves on the string

Answer 1

The linear density of the string is the following:

$$\mu = \dfrac{m}{L}$$

where $m = 3.4g = 3.4\times 10^{-3}kg$ and $L = 0.69m$. The speed of waves is given then as follows:

$$v = \sqrt{\dfrac{T}{\mu}} = \sqrt{\dfrac{TL}{m}}$$

where $T = 150N$.

Thus, obtain:

$$v = \sqrt{\dfrac{150N\cdot 0.69m}{3.4\times 10^{-3}kg}} \approx 1.7\times 10^2m/s$$

Answer. $1.7\times 10^2m/s$.