A transverse wave propagating on a stretched string of linear density 3 × 10 - 4 kgm - 1 is represented by the equation y = 0 . 2 sin ( 1 . 5 x + 60 t ) where, x in metres and t is in seconds. The tension in the string (in Newton) is

Step-by-step solution

Equation of wave, y = 0 . 2 sin [ 1 . 5 x + 60 t ] Comparing with standard equation, we get y = A sin [ k x + ω t ] k = 1 . 5 = 2 π λ and ω = 60 = 2 π T ∴ Velocity of wave, v = ω k = 60 1 . 5 = 40   m   s - 1 Velocity of wave in stretched string, v = T m where, m is the linear density, T is tension in the string. So, T = v 2 m = ( 40 ) 2 × 3 × 10 - 4 = 0 . 48   N