Four pieces of string of length L are joined end to end to make a long string of length 4L. The linear mass density of the strings are `mu,4mu,9mu and 16mu`, respectively. One end of the combined string is tied to a fixed support and a transverse wave has been generated at the other end having frequency `f` (ignore any reflection and absorption). string has been stretched under a tension `F`. Find the time taken by wave to reach from source end to fixed end.

Options

A. `(25)/(12)xx(L)/sqrt(F//mu)`
B. `(10L)/sqrt(F//mu)`
C. `(4L)/sqrt(F//mu)`
D. `(L)/sqrt(F//mu)`

Answer

b

Explanation

`v_(1)=sqrt((F)/(mu))`
`v_(2)=sqrt((F)/(4mu))=(1)/(2)sqrt((F)/(mu))`
`v_(3)=sqrt((F)/(9mu))=(1)/(3)sqrt((F)/(mu))`
`v_(4)=sqrt((F)/(16mu))=(1)/(4)sqrt((F)/(mu)`
Total time taken
`=(L)/(v_(1)+(L)/(v_(2)+(L)/(v_(3)+(L)/(v_(4)=(10L)/(sqrt(F//mu))`