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Power of waves


Consider a string with length \(2.8\text{ m}\) and mass \(280\text{ g}.\) The tension in the string is \(38.0\text{ N}.\) If a wave traveling along the string has an amplitude of \(7.7\text{ mm},\) what must be the frequency of the wave for the average power to be \(85.0\text{ W}?\)

Consider a string with linear density \(6.0\text{ g/m}\) and tension \(3375\text{ N}.\) If we send two identical sinusoidal waves of angular frequency \(1500\text{ rad/s}\) and amplitude \(4.0\text{ mm}\) simultaneously, i.e. their phase difference is \(0\), what is the approximate total average rate at which they transport energy?

If we send a sinusoidal wave with frequency \(f=120\text{ Hz}\) and amplitude \(y_m=10.5\text{ mm}\) along a string which has linear density \(\mu=545.0 \text{ g/m}\) and is under tension \(\tau=50.0\text{ N},\) approximately at what rate does the wave transport energy?

Suppose that energy is transmitted at rate \(P_1\) by a wave of frequency \(f_1\) on a string under tension \(\tau_1.\) If the tension is increased to \(\tau_2=16\tau_1\) and the frequency is decreased to \(f_2=f_1/3,\) what is the new energy transmission?

A transverse sinusoidal wave with frequency \(60 \text{ Hz}\) and amplitude \(0.40\text{ cm}\) is generated at one end of a long and horizontal string. The string has linear density \(90.0 \text{ g/m}\) and is kept under a tension of \(50.0\text{ N}.\) Approximately, what is the maximum rate of energy transfer along the string?


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