Question

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

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

Answer 1

Answer: (A)

Here,
Mass of the string, $m = 3\, kg$
Length of the string, $L =25\, cm= 25 \times 10^{-2}\,m$
Tension in the string, $T = 400\, N$
Mass per unit length of the string,
$\mu =\frac{m}{L} =\frac{ 3 \,kg}{25\times10^{-2} m} = 12 \,kg m^{-1}$
Speed of the wave on the string is
$ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{400\, N}{12\, kg \,m^{-1}}} = 5.77 \,m \,s^{-1} $
Time taken by disturbance to reach the other end
$t= \frac{L}{v} =\frac{ 25 \times 10^{-2}\, m}{5.77 \,m \,s^{-1}} $
$= 0.043 \,s$