Answer to Question #157722 in Mechanics | Relativity for Samir khan

Question

A string on a cello has a tension of 34.5N. The linear density is 0.05g / m . What is the speed of sound along the string ? 

Answer 1

The speed of sound along a string under tension can be found with the equation (https://pressbooks.online.ucf.edu/osuniversityphysics/chapter/16-3-wave-speed-on-a-stretched-string/):

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

where $T = 34.5N$ is the tension in the string, and $\mu = 0.05g/m = 5\times 10^{-5}kg/m$ is the  linear density of the string. Thus, obtain:

$$v = \sqrt{\dfrac{34.5N}{5\times 10^{-5}kg/m}} \approx 830.7 m/s$$

Answer. 830.7 m/s.