A water wave traveling in a straight line on a lake is described by the equation

Question

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

Explanation / Answer

y = 3.75 cm cos(0.450 x + 5.40 t)

y = A cos(kx + w t)

(A) T = 2pi / w =2 pi / 5.40 = 1.16 sec

(B) Horizontal distance = wavelength = 2 pi / k

=2 pi / 0.450

= 14 cm
= 0.14 m

(C) k = 0.450 rad/cm

(D) f = 1 / T = 0.862 waves /s

(e) v = lambda / T = 0.14 / 1.16 = 0.12 m/s

(f) Vmax = A w = (3.75 x 10^-2 m )(5.40)

= 0.20 m/s

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