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?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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, $t=\frac{l}{v}=\frac{20}{40}=0.50 \,s$

Similar Questions

Two pulses travel in mutually opposite directions in a string with a speed of $2.5 cm/s$ as shown in the figure. Initially the pulses are $10cm$ apart. What will be the state of the string after two seconds

Obtain the equation of speed of transverse wave on tensed (stretched) string.

A perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the pulse will

A wire of variable mass per unit length $\mu = \mu _0x$ , is hanging from the ceiling as shown in figure. The length of wire is $l_0$ . A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other ends

A string of length $1 \mathrm{~m}$ and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $\mathrm{T}$. when the string vibrates, two successive harmonics are found to occur at frequencies $750 \mathrm{~Hz}$ and $1000 \mathrm{~Hz}$. The value of tension $\mathrm{T}$ is. . . . . . .Newton.

  • [IIT 2023]