Question

A one-metre long stretched string having a mass of $40g$ is attached to a tuning fork. The fork vibrates at $128Hz$ in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

Answer 1

Step 1. Given data

A string of mass $m=(40\times {10}^{-3})kg$ is attached to the tuning fork.

Frequency of fork, $f=128Hz$

Number of loops, $n=4$

Length of string, $L=1m$

Step 2. Finding the tension in the string

Using relation,

$\begin{array}{rcl}\lambda & =& 2L/n\\ & =& 2x1/4\\ & =& 0.5m\\ & & \end{array}$

Also, we know,

$\begin{array}{rcl}v& =& f\lambda =\sqrt{(T/m)}\\ & \Rightarrow & T=f^{2}x{\lambda }^{2}xm\\ & \Rightarrow & T={\left(128\right)}^{2}x{\left(0.5\right)}^{2}x40x{10}^{-3}\\ & \Rightarrow & T=164N\end{array}$

Thus, the tension in the string is $164N$