Question

A string of mass $3kg$ is under the tension of $400N$. The length of the stretched string is $25cm$. If the transverse jerk is stuck at one end of the string, how long does the disturbance take to reach the other end?

• A. $0.043s$
• B. $0.055s$
• C. $0.034s$
• D. $0.065s$

Answer 1

The correct option is A

$0.043s$

Step 1: Given data

Mass of the string, $M=3kg$

Length of the string, $L=25cm$

$\Rightarrow L=25\times {10}^{-2}m$

Tension, $T=400N$

Step 2: Find the velocity of the wave,

Mass per unit length of the string, $\frac{m}{L}=\frac{3}{25\times {10}^{-2}}$

$\frac{m}{L}=12kg/m$

Velocity of the wave, $v=\sqrt{\frac{TL}{m}}$

$$\begin{gathered} \Rightarrow v=\sqrt{\frac{400}{12}} \\ \Rightarrow v=5.77m/sec \end{gathered}$$

Step 3: Find the time taken

Time taken,$t=\frac{L}{v}$

$$\begin{gathered} \Rightarrow t=\frac{0.25}{5.77} \\ \Rightarrow t=0.043s \end{gathered}$$

Hence, option (A) is correct.