Question

A cello string vibrates in its fundamental
mode with a frequency of 242 1/s. The vibrating segment is 91 cm long and has a mass
of 0.82 g.
Find the tension in the string.
Answer in units of N

Find the frequency of the string when it
vibrates in three segments.
Answer in units of 1/s.

Answer 1

Let's calculate $\mu$ =$\frac{0.82\times10^{-3}}{0.91}=0.9\times10^{-3}$

$v=\frac1{2l}\sqrt{\frac{T}{\mu}}=\frac{1}{2\times0.91}\sqrt{\frac{T}{0.9\times10^{-3}}}$

$242\times2\times0.91\times30=\sqrt T\\\sqrt T=13213.2\\T=174588654.24 N$

when string is divided into 3 segments then the frequency becomes 3 times of fundamental frequency

then the frequency is 3$\times242$ =726 Hz