Chapter 12, Problem 24P

To determine

To Calculate: The tension of the string.

Answer to Problem 24P

The tension force is $87\text{}\text{N}$ .

Explanation of Solution

Given:

The frequency is, $f=440\text{Hz}$

The length of the string, $l=32\text{cm}=0.32\text{m}$

The mass is, $m=0.35\text{g}$

Formula used:

The frequency is,

  $f=\frac{v}{2L}=\frac{1}{2L}\sqrt{\frac{F_T}{\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$L$}\right.}}$

Where, $F_T$ is the tension force

L is the length of the string

m is the masse of the vibrating portion of the string

Calculation:

By substituting the given values in the formula, the tension force is,

  $\begin{array}{l}{F}_T=4mL{f}^2\\ =4\times \left(0.35\text{g}\times {10}^{-4}\text{kg}\right)\times 0.32\text{m}\times {\left(0.32\text{m}\right)}^2\\ =87\text{N}\end{array}$

Conclusion:

The force is $87\text{N}$ .