A stretched rope having linear mass density 5 × 10 - 2   kg   m - 1 is under a tension of 80   N . The power that has to be supplied to the rope to generate harmonic waves at a frequency of 60   Hz and an amplitude of 6   cm is

Step-by-step solution

v = T μ = 80 5 × 10 - 2 = 40   m   s - 1 P = 1 2 ρ ω 2 A 2 S v = 1 2 μ 2 π f 2 v (as ρ S = μ ) = 1 2 × 5 × 10 - 2 2 π × 60 2 × 40 × 0 . 06 2 = 512   W .