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

Answer

B

Explanation

We use
y = 0.02 sin (x + 30t) for the given wave :
`v = (dx)/(dt) = -30` (As x + 30 t = constant)
we have speed `v = sqrt((T)/(mu))`
implies ` T = muv^(2) = A.rhoV^(2)`
= `(10^(-6)m^(2))(8 xx 10^(3)(kg)/(m^(3)))(30)^(2)`
implies T = 7.2N