A composite wire is made by joining two uniform wires. If `l_1 = l_2= l` and ` mu_1 = mu_2 /9 = mu`. Tension in the strings is T , `mu` is mass per unit length. Then lowest frequency such that the junction is an antinode.

Options

A. `1/(4l) sqrt(l/(mu))`
B. `3/(4l)sqrt(l/(mu))`
C. `5/(4l) sqrt(l/(mu))`
D. `7/(4l)sqrt(l/(mu))`

Answer

A

Explanation

For antinode
`f_(1)=((2n_(1)-1))/(4l)sqrt(l/(mu))`
`f_(2)=((2n_(2)-1))/(4l)sqrt(l/(9mu)) =((2n_(2)-1))/(12l)sqrt(l/(mu))`
`f=1/(4l)sqrt(l/(mu)) ((2n_(1)-1))/(4l)=(2n_(2)-1)/(12l)`
`6n_(1)-3 =2n_(2) -1`
`6n_(1)-2n_(2) =2 " " n_(1)=1, n_(2)=2`
`3n_(1)-n_(2)=1`,