 Classical Mechanics

# 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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