The transverse displacement of a string of a linear dinsity `0 . 0 1kgm^(-1)` , clamped at its ends is given by `Y _(x,t)= 0 . 0 3 sin((2pi x)/(3)) cos (60 pi t)` , where x and y arein metres and time t is in seconds . Tension in the string is

Options

A. 9 N
B. 36 N
C. 162 N
D. 81 N

Answer

D

Explanation

Transverse displacement
`y_((x,y)) = 0 .03 sin ((2 pi x)/(3)) cos 60 pi t `
Linear density = 0 . 0 1 kg/m `y = a sin kx cos omega t`
Velocity, `v = sqrt((T)/(mu)) = (omega)/(k)`
`:. sqrt((T)/(mu)) = (omega)/(k) ` [Here , `mu` = mass per unit length]
Here, `omega = 60 pi, k = 2 pi //3`
` sqrt((T)/(0 . 0 1)) = (60 pi)/(2pi //3)`
= 90
`(T)/(0 . 1) = 90 xx 90 `
`T = 90 xx 90 xx 0 . 01`
= 81 N