Question

A taut string for which $\mu =5.00\times {10}^{-2}kg/m$ is under a tension of 80.0 N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00 cm ?

Answer 1

Speed of waves in the string=$\sqrt{\frac{T}{\mu }}=\sqrt{\frac{80}{5\times {10}^{-2}}}=40m/s$

$\omega =2\pi \nu =2\times \pi \times 60Hz=377s^{-1}$

Power,$P=\frac{1}{2}\mu {\omega }^2{A}^{2}v$

$=\frac{1}{2}\times 5\times {10}^{-2}\times {377}^2\times {0.06}^2\times 40=512W$