Subjective Type

A string along which waves can travel is 2.70 m long and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mm for the average power to be 85.0 W?

Solution

Using Eq. for the average power and Eq. for the speed of the wave, we solve for $$f = \omega/2\pi$$ :
$$f = \dfrac{1} {2\pi y_m} \sqrt{\dfrac{2 P_{avg}} {\mu \sqrt{\tau/\mu}}} = \dfrac{1} {2\pi\left (7.70 \times 10^{-3} \space m \right )} \sqrt{\dfrac{2\left (85.0 \space W \right )} {\sqrt{\left (36.0 \space N \right ) \left (0.26 \space kg / 2.70 \space m \right )}}} = 198 \space Hz$$.

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