Physics - Wave on String Question with Solution | TestHub

The tension $T$ in the rope at a distance $x$ from its lower end is due to the weight of the rope below that point.

$T=\mu xg$

where $\mu$ is the linear mass density of the rope.

The speed of a transverse wave at a distance $x$ from the lower end is given by:

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{\mu xg}{\mu }}=\sqrt{xg}$

At the upper end, the distance from the lower end is $x=2.5$ m.

$v_{upper}=\sqrt{2.5\times 10}=\sqrt{25}=5$ m/s

At a distance $x=0.5$ m from the lower end:

$v_{lower}=\sqrt{0.5\times 10}=\sqrt{5}$ m/s

Answer: $5$ m/s, $\sqrt{5}$ m/s