Question

A uniform string of length $20m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is: (take $g=10m/s^2$ )

• A. $2\pi \sqrt{2}s$
• B. $\sqrt{2}s$
• C. $2s$
• D. $2\sqrt{2}s$

Answer 1

The correct option is D $2\sqrt{2}s$

Let linear mass density $(\text{mass/length}$ is $\mu$.

Consider $x$ length of the string, the
tension at this position is $T$.

$T=\left(x\mu \right)g$
The velocity of wave pulse

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{\left(x\mu \right)g}{\mu }}=\sqrt{gx}$
$\frac{dx}{dt}=\sqrt{gx}$
$\Rightarrow \frac{dx}{\sqrt{x}}=\sqrt{gdt}$

On solving we get, $t=2\sqrt{2}s$

Final answer: (c)