Question

A string of mass $3kg$ is under 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

Answer: (A)

Here,
Mass of the string, $m=3kg$
Length of the string, $L=25cm=25\times 10^{-2}m$
Tension in the string, $T=400N$
Mass per unit length of the string,
$\mu =\frac{m}{L}=\frac{3kg}{25\times 10^{-2}m}=12kg{m}^{-1}$
Speed of the wave on the string is
$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{400N}{12kg{m}^{-1}}}=5.77m{s}^{-1}$
Time taken by disturbance to reach the other end
$t=\frac{L}{v}=\frac{25\times 10^{-2}m}{5.77m{s}^{-1}}$
$=0.043s$