The equation of a wave on a string of linear mass density 0.04 kg `m^(-1)` is given by `y=0.02(m)sin[2pi((t)/(0.04(s))-(x)/(0.50(m)))]`. The tension in the string is

Options

A. 4.0N
B. 12.5N
C. 0.5N
D. 6.25N

Answer

D

Explanation

The given equation of a wave is `y = 0.02 sin[2 x ((t)/(0.04)-(x)/(0.50))]`
Compare it with the standard wave equation `y= a sin(omega t - kx)`
We get : `omega = (2x)/(0.04)rads^(-1) , k=(2 pi)/(0.5) rads^(-1)`
Wave velocity , `v = (omega)/(k) = ( (2 pi) // (0.04))/((2 pi) // (0.5)) ms^(-1)` .. (i)
Aiso `v = sqrt((T)/(mu))` ..(ii)
Where T is the tension in the string and `mu` is the linear mass density. Here, linear mass density ` mu = 0.04 kgm^(-1)`
Equating equation (i) and (ii), we get :
`(omega)/(k)= sqrt((T)/(mu)) or T = (mu omega^(2))/(k^(2)), T=(0.04 xx((2pi)/(0.04))^(2))/((2 pi)/(0.5))^(2) = 6.25N`.