Question 203: Waves

Question

A uniform string of length $$20$$ $$m$$ 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 supports is : 
(take $${\,\,g = 10m{s^{ - 2}}}$$ )

Accepted Answer

We know that velocity in string is given by
$$v = \sqrt {{T \over \mu }} \,\,\,\,\,\,\,\,\,\,\,\,....\left( i ight)$$
where $$\mu  = {m \over {m I}} = {{mass\,\,\,of\,\,\,string} \over {length\,\,\,of\,\,\,string}}$$
The tension $$T = {m \over \ell } 	imes x 	imes g\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)$$
From $$(a)$$ and $$(b)$$ $${{dx} \over {dt}} = \sqrt {gx} $$
$${x^{ - 1/2}}\,dx = \sqrt g \,dt$$
$$	herefore$$ $$\int\limits_0^\ell  {{x^{ - 1/2}}} dx - \sqrt g \int\limits_0^\ell  {dt} $$
$$2\sqrt \ell   = \sqrt g  	imes t$$
$$	herefore$$ $$t = 2\sqrt {{\ell  \over g}}  = 2\sqrt {{{20} \over {10}}}  = 2\sqrt 2 $$

Answer

$$2\sqrt 2 s$$

Answer

$$2\pi \sqrt 2 s$$

Answer

$$2\pi \sqrt 2 s$$

Answer

$$2$$ $$s$$

Waves

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

Choose the correct answer: