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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)). |
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Answer» Solution :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`. |
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