Question

A cello string vibrates in its fundamentalmode with a frequency of 178 1/s. The vibrating segment is 106.7 cm long and has amass of 1.04 g.Find the tension in the string.Answer in units of N.

Answer 1

Give data:

The frequency of vibration is f=178 1/s.

The length of vibrating segment is l=106.7 cm.

The mass of the string is m=1.04 g.

The tension in the string can be calculated as,

$f=\frac{1}{2l}\sqrt[]{\frac{TL}{m}}$

Substitute the given valuse in above equation,

$\begin{gathered} 178=\frac{1}{2(106.7cm\times\frac{1\text{ m}}{100cm})}\sqrt[]{\frac{T(106.7cm\times\frac{1\text{ m}}{100cm})}{(1.04g\times\frac{1kg}{1000g})}} \\ T=140\text{ N} \end{gathered}$

Thus, the tension in the string is 140 N.