Question

Find the speed of a transverse wave that is in a 3 m string and has a mass of 0.130 kg if it can withstand a tension of 500 N.

Answer 1

The speed of the wave in a string is given as follows (see https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/16-3-wave-speed-on-a-stretched-string/):

$$v = \sqrt{\dfrac{F}{\mu}}$$

where $F = 500N$ is the tension in the string, and $\mu$ is the linear mass density.

By definition, have:

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

where $m = 0.130kg$ is the total mass of the string, and $L = 3m$ is its total length.

Thus, obtain:

$$v = \sqrt{\dfrac{FL}{m}}\\ v = \sqrt{\dfrac{500N\cdot 3m}{0.13kg}} \approx 107m/s$$

Answer. 107m/s.