A string of mass $2.50 \;kg$ is under a tension of $200\; N$. The length of the stretched string is $20.0 \;m$. If the transverse jerk is struck at one end of the string, how long (in $sec$) does the disturbance take to reach the other end?
A string of mass $2.50 \;kg$ is under a tension of $200\; N$. The length of the stretched string is $20.0 \;m$. If the transverse jerk is struck at one end of the string, how long (in $sec$) does the disturbance take to reach the other end?
Mass of the string, $M=2.50\, kg$
Tension in the string, $T=200\, N$
Length of the string, $l=20.0\, m$
Mass per unit length, $\mu=\frac{M}{l}=\frac{2.50}{20}=0.125\, kg\, m ^{-1}$
The velocity $(v)$ of the transverse wave in the string is given by the relation:
$v=\sqrt{\frac{T}{\mu}}$
$=\sqrt{\frac{200}{0.125}}=\sqrt{1600}=40 \,m / s$
$\therefore$ Time taken by the disturbance to reach the other end, $t=\frac{l}{v}=\frac{20}{40}=0.50 \,s$
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