Waves and A Fisherman on a boat

[Punkyc7]

a water wave is traveling in a straight line on a lake is described by the equation
y(x,t)=.0375mcos(.0045 m^-1 (x) + 5.4 s^-1 (t))

How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor, and what is the horizontal distance does the wave crest travel in that time.

My question is about the second part of the question.

for the first part I got 2Pi/5.4=t

so for the horizontal distance is it just .0045*((2Pi)/5.4)

 

[ideasrule]

No, because 0.0045 m^-1 isn't the speed of the wave (and it doesn't have the right units).

0.0045 m^-1 is k and wavelength is 2*pi/k. Is it intuitive that one wavelength passes the fisherman in the time it takes a complete cycle to go past?

 

[Punkyc7]

So was my time right?

so if lambda = 2*pi/k

would that mean the distance would be 1396.263?

 

[ideasrule]

Yes.