A metallic rod of length $\mathcal{l}$  , linear mass density $\mu$  rotates about one of its end ‘O’ in a smooth horizontal plane with an angular velocity $\omega$  about an end axis which is perpendicular to plane of rotation shown in figure. A transverse pulse generated at the free end P to reach the axis of rotation.  (neglect the gravitational effect). 

The speed of the transverse pulse when it reaches the midpoint of sting with respect to ground is    
$\frac{\sqrt{5}l\omega }{\sqrt{8}}$

The tension in the string at a distance ‘x’ from the free end   $\frac{\mu [l^2-{(l-x)}^2]}{2}{\omega }^2$

The speed of the transverse pulse just after generated at the free end point P with respect to ground is  $l\omega$  
 

The time taken by the transverse pulse to reach the axis of rotation from free end is  $\frac{\pi }{\sqrt{2}\omega }$