A string is hanging from a rigid support. A transverse
pulse is excited at its free end. The speed at which the
pulse travels a distance x is proportional to

Options

A. x
B. `(1)/(x)`
C. `(1)/(sqrt(x))`
D. `sqrt(x)`

Answer

D

Explanation

The speed of travel of a pulse in a string is `v=sqrt((T)/(mu))`
The tension at a point is proportional to the weight acting down at that point. At the top, it is maximum. At a distance x from the bottom, `T=muxg` where `mu` = mass per unit length.
`therefore v=sqrt((muxg)/(mu))orvpropsqrt(x)`