 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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