Question

A stretched rope having linear mass density $5\times {10}^{-2}kg{m}^{-1}$ 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 (nearly)

• A. 215 W
• B. 251 W
• C. 10368 W
• D. 521 W

Answer 1

The correct option is C 10368 W

Power $P=2{\pi }^2{A}^2{v}^{2}V\mu$

$=2\times (3.14{)}^2\times (6\times {10}^{-2}{)}^2\times (60{)}^2\times \sqrt{\frac{T}{\mu }}\times \mu$

$=2\times (3.14{)}^2\times (6\times {10}^{-2}{)}^2\times (60{)}^2\times \sqrt{5\times {10}^{-2}\times 80}$

$=10.368\times {10}^3$

$=10368W$