A reniform rope of mass 0.7 kg and length 2.45 in hangs from a ceiling (a) Find the speed of Transverse wave in the rope at a point 0.5m distrus from the lower end, b) Puste Calculate the time taken by a transverse wave to travel the full length of the rope `(g=9.8m//s^(2))`.

Explanation

Suppose the `.mu.` be the linear density of rope. Let T be the tension at a point .p. at a distance .x. from lower end of rope.
The tension is `T= x mug`
The vel. Of wave at the point is
`v=sqrt((T)/(mu))= sqrt((muxg)/(mu))= sqrt(xg)`
At `x=0.05m v= sqrt(0.5xx9.8)=2.21m//s`
At lower end u=0 Attop end `v= sqrt(gl)`
`a=(v^(2)-u^(2))/(2s)=(gl-0)/(2l)=(g)/(2)`
time taken to travel the wave from lower end to upper end is `t=(v-u)/(a)=(sqrt(gl)-0)/(g//2)=2 sqrt((l)/(g))=2 sqrt((2.45)/(9.8))= 1 sec`.