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 ratio of wavelength of the wave on four string, starting from right hand side.

Options

A. `12:6:4:3`
B. `4:3:2:1`
C. `3:4:6:12`
D. `1:2:3:4`

Answer

C

Explanation

Frequency of wave is same on all the four string. So,
`lambda_(1)=(v_(1))/(f), lambda_(2)=(v_(2))/(f)`
`lambda_(3)=(v_(3))/(f) lambda_(4)=(v_(4))/(f)`
`lambda_(4), lambda_(3), lambda_(2), lambda_(1)=(1)/(40:(1)/(3):(1)/(2):1=3:4:6:12`