Waves passing a fisherman boat

In summary, we have been given an equation for a wave traveling on the ocean and are asked several questions about it. To find the time for one complete wave pattern to pass the fisherman, we can set the equation equal to 0 and use the fact that cos(pi/2) = 0. From this, we can find the period of the wave. To find the horizontal distance traveled, we can use the equation for wave velocity to find the distance traveled in the time found previously. The wave number can be found by comparing the given equation to the standard equation for a progressive wave. The number of waves per second can be found by using the period found earlier. Finally, the maximum speed of the cork floater can be found
  • #1
Heat
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0

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?
 
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  • #2
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.
 
  • #3
I do not follow...

I understand the general equation, and how it is related but I cannot see now I would find it.
 
  • #4
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.
 
Last edited:

1. How do waves affect a fisherman's boat?

Waves can cause a fisherman's boat to rock back and forth, potentially making it difficult to maintain balance and stability. Large waves can also pose a danger to smaller boats and may cause them to capsize.

2. How do different types of waves impact a fisherman's boat?

The impact of waves on a fisherman's boat can vary depending on the type of wave. For example, choppy waves can cause a boat to bounce and sway, while larger swells can create a rolling motion. Wind-driven waves may also push a boat off course or create turbulence in the water.

3. Can a fisherman's boat capsize from waves?

Yes, a fisherman's boat can capsize if it encounters large or powerful waves. It is important for fishermen to be aware of weather conditions and to navigate their boats carefully to avoid potential capsizing.

4. How can a fisherman prepare for waves while on the water?

Fishermen can prepare for waves by checking weather forecasts and avoiding areas where large or dangerous waves are expected. It is also important to have proper safety equipment on board and to know how to navigate through waves safely.

5. Are there any techniques for navigating through waves in a fisherman's boat?

Yes, there are techniques for navigating through waves in a fisherman's boat. These include keeping a steady speed, steering into the waves at an angle, and using the boat's momentum to help it ride over the waves. It is also important to distribute weight evenly on the boat to maintain balance and stability.

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