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Q. A transverse wave pulse is generated at the free end of a string which is hanging from a rigid support. The speed of the wave pulse at distance $x$ from the free end is proportional to

NTA AbhyasNTA Abhyas 2020Waves

Solution:

At x distance from end
$\text{Velocity in string} = \sqrt{\frac{\text{Tension}}{\text{Mass per unit length}}}$
$v=\sqrt{\frac{T}{\mu }}$
Solution
$v=\sqrt{\frac{\mu x g}{\mu }} \, $
$v=\sqrt{x g}$
$v \propto \sqrt{x}$