# Homework Help: Amplitude of a wave hitting a boat

1. Nov 15, 2008

### itryphysics

1. The problem statement, all variables and given/known data
You are finding it a challenge to climb from one boat up onto a higher boat in heavy waves.
If the climb varies from 2.1 m to 4.5m , what is the amplitude of the wave? Assume the centers of the two boats are a half wavelength apart.

2. Relevant equations

just used simple arithmatic

3. The attempt at a solution
so since the starting point will be 2.1 m, i assumed that to get the amplitude i would only have to subtract that from the height of the higher boat. so 4.5 - 2.1 = 2.4

2. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

HINT: The boats are half a wavelength apart.

3. Nov 15, 2008

### itryphysics

Re: amplitude

so 2.4 divided by 2? :S

4. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Not quite. The question states the difference in the height between the two boats varies from 2.1m to 4.5m. This is not the same as the positions of the boats. In other words, the maximum vertical distance between the two boats is 4.5m and the minimum is 2.1m.

Do you follow?

5. Nov 15, 2008

### itryphysics

Re: amplitude

hmmm... so if 2.1 is the minimum does that mean from the bottom of one boat to the bottom of the other? and then maximum is from the bottom of the first boat to the top of the second boat?

actually im not quite sure I follow

6. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

No. As the question says, these distances are measured to the centre of each boat. The vertical distance between the boats depends on their position of the wave.

To illustrate this, sketch a sine wave and draw two dots on the wave separated by half a wavelength. Now shift both points the same distance to the right along the wave and draw two new points. Now measure the vertical distance between the first two dots and then do the same for the second two dots. Compare the vertical distances between the two sets of dots.

Do you see?

7. Nov 15, 2008

### itryphysics

Re: amplitude

The vertical distance between the two points in each set remains the same. right?

8. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

No, not in general.

9. Nov 15, 2008

### itryphysics

Re: amplitude

well the points swap positions. im not sure what you are getting at. can you please give another example or perhaps elaborate more on this one

10. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Okay, more specific.

1. Plot y=sin(x)
2. Plot the points (x,y)=(0,0) and (x,y)=(pi,0) - this is group A
3. Plot the points (x,y)=(pi/2,1) and (x,y)=(3pi/2, -1) - this is group B
4. What is the vertical distance between the points in group A?
5. What is the vertical distance between the points in group B?

Do you see now?

11. Nov 15, 2008

### itryphysics

Re: amplitude

vertical distance b/w group A is zero and b/w group B is 2

12. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Correct. So even though the points in both groups are separated by half a wavelength (pi) their vertical distances are not necessarily equal - they depend on the position of the two points, not just their relative position.

Does that make sense now?

13. Nov 15, 2008

### itryphysics

Re: amplitude

yes I understand now. How do I go about figuring out the position of the two points?

14. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Again think of the sine curve. At which two points on the curve is the vertical distance between these point maximum and what value does it correspond to?

15. Nov 15, 2008

### itryphysics

Re: amplitude

max distance would be (pi/2, 1) (3pi/2,-1)
so a vertical distance of 2

16. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Correct. So how does this value of 2 correspond to the amplitude?

17. Nov 15, 2008

### itryphysics

Re: amplitude

oh so the amplitude will be twice the distance between them?

18. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

Not quite. What is the definition of amplitude?

19. Nov 15, 2008

### itryphysics

Re: amplitude

amplitude: The maximum height of a crest or depth of a trough, relative to the normal level.

20. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

And where is the normal level in this case?

21. Nov 15, 2008

### itryphysics

Re: amplitude

zero?

22. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

If that were the case, then the minimum separation between the boats would be zero, as for the sine exercise we did earlier.

23. Nov 15, 2008

### itryphysics

Re: amplitude

Im a bit lost. so we established that the maximum vertical distance between the two boats is 2. The distance from the center of each boat is 2.1m-4.5m = 2.4 m How can that be?

24. Nov 15, 2008

### Hootenanny

Staff Emeritus
Re: amplitude

No we didn't, that was just in the exercise that I gave you to illustrate that the vertical distance depends on the absolute position of each boat, not the relative position.

Edit: Hang on a minute, I made need to re-think our approach.

25. Nov 15, 2008

### itryphysics

Re: amplitude

so is the normal level 2.1 then?