How Do Waves Affect a Fisherman's Boat?

[Heat]

Homework Statement

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

y ( x,t) = (3.75cm)cos(.450cm^-1x + 5.40s^-1t)
where y is the displacement perpendicular to the undisturbed surface of the ocean.


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

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

What is the wave number?

What isthe 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?

The Attempt at a Solution

ok for part a this is my attempt

since it says that the following y ( x,t) = (3.75cm)cos(.450cm^-1x + 5.40s^-1t)

the y will be the same, as when the period/cycle ends it will be in the same position and the x will also be the same as the boat is anchored.

so it should be safe to assume

0 = 3.75 cos (t/5.40s)

cos is equal to 0 when it's is one

cos pi/2 = 0

pi/2 = t / 5.40

t = 8.48

does this seem right?

 

[rl.bhat]

Equation of a progressive wave is given by Y(x,t) = Acos(2*pi*x/lamda + 2*pi*t/T). If you compare this with the given equation you can find T. peroid of the wave. And it is required in the first question.

 

[Heat]

I do not follow...

I understand the general equation, and how it is related but I cannot see now I would find it.

 

[rl.bhat]

y ( x,t) = (3.75cm)cos(.450cm^-1x + 5.40s^-1t) If you comare the two equation we have 2pi/lamda = 0.450 from this find wavwlengh lamda. And 2*pi/T = 5.4s^-1, from this find period T.