A string is hanging from a rigid support. A transverse wave pulse is set up at the free end. The velocity…
A string is hanging from a rigid support. A transverse wave pulse is set up at the free end. The velocity $v$ of the pulse related to the distance $x$ covered by it is given as
$v \propto \sqrt{x}$
$v \propto x$
$v \propto \frac{1}{x}$
None of these
Solution
Diagram shows a vertical rope fixed at top ceiling with coordinate x measured from bottom free end where weight m_x g acts, and tension T pulling upwards.
Tension at distance $x$ from free end,
$T_x = w_x = m_x g = (\alpha x g)$
$\sqrt{\frac{T_x}{\alpha}} = \sqrt{x g}$ or $v = \sqrt{x g}$
$\therefore v \propto \sqrt{x}$