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) = (4.15 cm) cos(0.425 cm?1x + 5.35 s?1t)

where y is the displacement perpendicular to the undisturbed surface of the lake.

(a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?
1 s

What horizontal distance does the wave crest travel in that time?
2 m

(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?
5 m/s

What is the maximum speed of his cork floater as the wave causes it to bob up and down?
6 m/s

Explanation / Answer

T = 2*pie/w = 2*pie/5.35 = 1.17

k = 2*pie / lamda

lamda = 2*pie/0.425 = 14.78 cm

b) f = 1/T = w/2*pie = 5.35/2*3.1415

=0.85 hz

c) v = lamda*f = w/lamda = 5.35/0.425 = 12.58 cm/s

V_y max = A*w = 4.15*5.35 = 22.2

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