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Amplitude of a wave hitting a boat

  1. Nov 15, 2008 #1
    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
    This answer is incorrect. Please explain why.
     
  2. jcsd
  3. Nov 15, 2008 #2

    Hootenanny

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    Re: amplitude

    HINT: The boats are half a wavelength apart.
     
  4. Nov 15, 2008 #3
    Re: amplitude

    so 2.4 divided by 2? :S
     
  5. Nov 15, 2008 #4

    Hootenanny

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    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?
     
  6. Nov 15, 2008 #5
    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
     
  7. Nov 15, 2008 #6

    Hootenanny

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    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?
     
  8. Nov 15, 2008 #7
    Re: amplitude

    The vertical distance between the two points in each set remains the same. right?
     
  9. Nov 15, 2008 #8

    Hootenanny

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    Re: amplitude

    No, not in general.
     
  10. Nov 15, 2008 #9
    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
     
  11. Nov 15, 2008 #10

    Hootenanny

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    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?
     
  12. Nov 15, 2008 #11
    Re: amplitude

    vertical distance b/w group A is zero and b/w group B is 2
     
  13. Nov 15, 2008 #12

    Hootenanny

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    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?
     
  14. Nov 15, 2008 #13
    Re: amplitude

    yes I understand now. How do I go about figuring out the position of the two points?
     
  15. Nov 15, 2008 #14

    Hootenanny

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    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?
     
  16. Nov 15, 2008 #15
    Re: amplitude

    max distance would be (pi/2, 1) (3pi/2,-1)
    so a vertical distance of 2
     
  17. Nov 15, 2008 #16

    Hootenanny

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    Re: amplitude

    Correct. So how does this value of 2 correspond to the amplitude?
     
  18. Nov 15, 2008 #17
    Re: amplitude

    oh so the amplitude will be twice the distance between them?
     
  19. Nov 15, 2008 #18

    Hootenanny

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    Re: amplitude

    Not quite. What is the definition of amplitude?
     
  20. Nov 15, 2008 #19
    Re: amplitude

    amplitude: The maximum height of a crest or depth of a trough, relative to the normal level.
     
  21. Nov 15, 2008 #20

    Hootenanny

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    Re: amplitude

    And where is the normal level in this case?
     
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