A transverse wave described by equation `y=0.02sin(x+30t)` (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section `1mm^2` and density `8000kg//m^(2)`. What is the tension in the string?

Options

A. 20 N
B. 7.2 N
C. 30 N
D. 14.4 N

Answer

B

Explanation

`y=0.02 sin (x+30t)`
For the given wave
`v=(dx)/(dt)=-30` (`:' x+30 t`=constant)
we have, `v=sqrt(T/(mu))rArr T=mu v^(2) =A.rho v^(2)`
`=(10^(-6)m^(2))(8xx10^(3)(kg)/(m^(3)))(30)^(2)`
`rArr T=2.7 N`