A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed ( v ) of wave pulse varies with height h from the lower end as shown

Question

A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed ( v ) of wave pulse varies with height h from the lower end as shown in the figure.

TestHub · Accepted Answer

Let m be the total mass of the rope of length $l$ . Tension in the rope at a height h from lower end= weight of rope of length $h$ is $T = \frac{m g}{l} (h)$

As $v^{2} = g h$

Which is a parabola. Therefore, $h$ versus $v$ graph is a parabola option (a) is correct.

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