A perfectly elastic uniform string is suspend | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.At

Vedclass · Accepted Answer

both $(B)$ and $(C)$

Vedclass · Answer

(D) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.At a distance $x$ from the lower end,the tension $T(x) = w + \mu x g$,where $w$ is the weight attached at the lower end.Thus,$v = \sqrt{\frac{w + \mu x g}{\mu}} = \sqrt{\frac{w}{\mu} + xg}$.As the pulse travels upwards,$x$ increases,so the speed $v$ increases.Squaring both sides,$v^2 = \frac{w}{\mu} + xg$.Differentiating with respect to time $t$,$2v \frac{dv}{dt} = g \frac{dx}{dt}$.Since $\frac{dx}{dt} = v$,we have $2v \frac{dv}{dt} = gv$,which simplifies to $\frac{dv}{dt} = \frac{g}{2}$.Thus,the pulse travels upwards with a constant acceleration of $\frac{g}{2}$.

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

Similar Questions

$A$ string of mass $2.5 \, kg$ is under some tension. The length of the stretched string is $20 \, m$. If the transverse jerk produced at one end of the string takes $0.5 \, s$ to reach the other end,the tension in the string is .... $N$

$A$ wire of variable mass per unit length $\mu = \mu_0 x$ is hanging from the ceiling as shown in the figure. The length of the wire is $l_0$. $A$ small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach the other end.

$A$ string of length $1 \,m$ and mass $490 \,g$ is put under a tension of $25 \,N$. $A$ wave of frequency $120 \,Hz$ is sent along it. The speed of this wave is (in $\,m/s$)

If the initial tension on a stretched string is doubled,then the ratio of the initial and final speeds of a transverse wave along the string is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module