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Oscillations

# A taut string for which $\;\mu=5\times 10^{-2} \;Kg/m\;$ is under as tension of 80 N . How much power must be supplied to the string to generate a sinusoidal wave at a frequency of 60 Hz and an amplitude of 6 cm ?

$(a)\;512\;W\qquad(b)\;500\;W\qquad(c)\;640\;W\qquad(d)\;746\;W$

Answer : (a) $\;512\;W$
Explanation :
Velocity (v) = $\;\sqrt{\large\frac{T}{\mu}}=\sqrt{\large\frac{80}{5 \times 10^{-2}}}=40\;m/s$
$f=60\;Hz$
angular frequency (w) = $\;2 \pi f$
$=2 \pi \times 60=377\;s^{-1}$
Power (P) = $\;\large\frac{\mu w^2 A^2 v}{2}$
$=\large\frac{1}{2}\times (5 \times 10^{-2}) \times(377) \times (6 \times 10^{-2})^{2} \times 40$
$=512 W$