Question

A string of mass $2.50 \, kg$ is under a tension of $200 \, N$ . The length of the stretched string is $20 \, m$ . if the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

• A. $0.50s$
• B. $0.20s$
• C. $0.10s$
• D. $0.40s$

Answer 1

Answer: (A)

Velocity of transverse wave
$v = \sqrt{\frac{T ⁡}{\mu }}$
where, T = tension in the string = 200 N
μ= mass per unit length
$= \frac{\text{Mass}}{\text{Length}} = \frac{2 \cdot 5 0}{2 0} = 0 \cdot 1 2 5 \text{kg/m}$
$v = \sqrt{\frac{2 0 0}{0 \cdot 1 2 5}} = \sqrt{1 6 0 0} = 4 0 \text{m/s}$
Time taken by the disturbance to reach the other end
$t = \frac{l }{v ⁡} = \frac{2 0}{4 0} = 0 \cdot 5 0 \text{s}$