A transverse displacement of vibrating string is y=0.06 ( 2 3 ) x (120 t) . If the mass per unit length of a string is 4 10⁻² ~kg / m , then the tension in the string will be

Step-by-step solution

Given the transverse displacement y = 0.06 ( 2 3 x ) (120 t) , comparison with the standard standing wave form y = A (kx) ( t) identifies the wave number k = 2 3 rad/m and angular frequency = 120 rad/s. The wave speed follows from v = k = 120 2 3 = 180 m/s. For a string with mass per unit length = 4 10⁻² kg/m, the speed of transverse waves obeys v = T . Solving for tension yields T = v^2 = (180)^2 (4 10⁻²) = 1296 N. The tension in the string is 1296 N .