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Water wave traveling in a straight line on lake is cescribed by the equation y(x, t) = (3.43 cm) cos[(0.460 rad*cm-"x (4.48 rac*s-I)t], where y is the cisplace...

Question

Water wave traveling in a straight line on lake is cescribed by the equation y(x, t) = (3.43 cm) cos[(0.460 rad*cm-"x (4.48 rac*s-I)t], where y is the cisplacement perpencicular to the undisturbed surface of the ake. A fishermanis in boat at anchor on the surface of the water Whatis the maximum speec of the fishermans cork floater asthe wave causes itto bob up and down?

water wave traveling in a straight line on lake is cescribed by the equation y(x, t) = (3.43 cm) cos[(0.460 rad*cm-"x (4.48 rac*s-I)t], where y is the cisplacement perpencicular to the undisturbed surface of the ake. A fishermanis in boat at anchor on the surface of the water Whatis the maximum speec of the fishermans cork floater asthe wave causes itto bob up and down?



Answers

A water wave traveling in a straight line on a lake is described by the equation $$y(x, t)=(3.75 \mathrm{cm}) \cos \left(0.450 \mathrm{cm}^{-1} x+5.40 \mathrm{s}^{-1} t\right)$$ where $y$ is the displacement perpendicular to the undisturbed surface of the lake. (a) How much time does it take for one complete wave pattem to go past a fisherman in a boat at anchor, and what horizontal distance does the wave crest travel in that time? (b) What are the wave number and the number of waves per second that pass the fisherman? (c) How fast does a wave crest travel past the fisherman, and what is the maximum speed of his cork floater as the wave causes it to bob up and down?


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