Power of waves


Consider a string with length 2.8 m2.8\text{ m} and mass 280 g.280\text{ g}. The tension in the string is 38.0 N.38.0\text{ N}. If a wave traveling along the string has an amplitude of 7.7 mm,7.7\text{ mm}, what must be the frequency of the wave for the average power to be 85.0 W?85.0\text{ W}?

Consider a string with linear density 6.0 g/m6.0\text{ g/m} and tension 3375 N.3375\text{ N}. If we send two identical sinusoidal waves of angular frequency 1500 rad/s1500\text{ rad/s} and amplitude 4.0 mm4.0\text{ mm} simultaneously, i.e. their phase difference is 00, what is the approximate total average rate at which they transport energy?

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

Suppose that energy is transmitted at rate P1P_1 by a wave of frequency f1f_1 on a string under tension τ1.\tau_1. If the tension is increased to τ2=16τ1\tau_2=16\tau_1 and the frequency is decreased to f2=f1/3,f_2=f_1/3, what is the new energy transmission?

A transverse sinusoidal wave with frequency 60 Hz60 \text{ Hz} and amplitude 0.40 cm0.40\text{ cm} is generated at one end of a long and horizontal string. The string has linear density 90.0 g/m90.0 \text{ g/m} and is kept under a tension of 50.0 N.50.0\text{ N}. Approximately, what is the maximum rate of energy transfer along the string?


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