Question

A stretched rope having linear mass density $5\times {10}^{-2}kg{m}^{-1}$ is under a tension of 80N. Power (in Watts) $=648n{\pi }^2\times {10}^{-2}$ has to be supplied to the rope to generate harmonic waves at a frequency of 60Hz and an amplitude of 6 cm. The value of n is___

Answer 1

$P=\frac{1}{2}\rho A^2{\omega }^{2}sv$;

s – Area of cross-section of Rope

$=\frac{1}{2}\mu A^2{\omega }^{2}v=\frac{1}{2}\mu A^2{\omega }^2\sqrt{\frac{T}{\mu }}=5184{\pi }^2\times {10}^{-2}W$

Thus value of n is 5184/648 =8