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 figure.

Question

Dr. Abubacker · Accepted Answer

(a) 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 $T = \frac{mg}{l}(h)$
As $v = \sqrt{\frac{T}{(m/l)}}$
$v = \sqrt{\frac{mg(h)}{l(m/l)}} = \sqrt{gh}$
$v^{2} = gh$
Which is a parabola. Therefore, $h\ $ versus $v\ $ graph is a parabola option (a) is correct.

Q. 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 figure.

Explanation

Reviewed by Dr. Abubacker

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