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

Answer

A

Explanation

For a transvese wave along a string ` v = sqrt(T/m) `
The given equation is
` y = 0.02 sin [2pi (t/(0.04) - x/(0.5))]`
Comparing with `y = A sin 2 pi (t/T - x/lambda) ` , we get
period `T = 0.04 = 4/100 " " :. n = 100/4 = 25` Hz
and `lambda = 0.5 m " " :. v = n lambda = 25 xx 0.5 = 12.5` m/s
but `v = sqrt(T/m) " " :. v^(2) = T/m`
`:. T = v^(2) m`
` = 25/2 xx 25/2 xx 4/100 = 25/4 = 6.25 N `