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Waves are disturbances that transport energy without transporting mass. Learn the mechanism underlying sound, deep ocean swells, light, and even the levitation of objects in mid air.

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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