Question

A mass M is hanging from a rope of length L and mass m. A student gives the mass a quick horizontal shake to set up a wave which travels along the rope.Give an expression, in terms of the provided variables, for the speed of the wave at the bottom of the string. You may assume the mass of the rope m is much less than M

Answer 1

Step-by-step explanation:

Expression for velocity of wave produced in a hanging wire can be given as follows

Velocity v =
`\sqrt{(T)/(m) }`

where T is tension in wire and m is mass of wire per unit length.

In the given case

T = Mg + mg

= Mg

neglecting weight of rope

mass of the rope per unit length

= m / L

Velocity of wave

=
`\sqrt{(Mg)/((m)/(L) ) }`

=
`\sqrt{(MgL)/(m) }`