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Power of a Transverse wave question

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Problem: http://img355.imageshack.us/my.php?image=a3physicsfa1.png


    2. Relevant equations
    http://hyperphysics.phy-astr.gsu.edu/Hbase/Waves/powstr.html


    3. The attempt at a solution

    Yeah, can someone help me exactly to find the velocity I need in order to plug it in to the equation? I tried figuring out with the velocity using wavelength and all, but that didn't work. I think I need to sue that forumula, but without knowing T, I'm stumped right now.

    Also, what exactly is the difference between the maximum speed of this wave, and the speed calculated from, let's say

    V = sqrt (T/(M/L)) ?
     
  2. jcsd
  3. Nov 16, 2008 #2
    Please, need some help with this. >.>
     
  4. Nov 16, 2008 #3

    Redbelly98

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    You can get the propagation velocity from wavelength and frequency. Can you show how you tried that, or just where you were stumped in your attempt?
     
  5. Nov 16, 2008 #4

    Doc Al

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    The speed of the wave pulse is contained in the [tex]\sin (kx - \omega t)[/tex] factor. How do k and ω relate to wavelength and frequency?

    Read this: Traveling Wave Parameters
     
  6. Nov 16, 2008 #5
    Ok, what exactly is this "propogation velocity". I've never heard of this term before, and I find it very... odd. Is it like initial velocity, average velocity, etc.

    I know that k= 2pi/(wavelength)

    I also know that f =w/2pi

    I also know that v = (wavelength)*(frequency)

    My question is, is that v the "propogation" velocity (the one in the above equation), whatever that means. Cause I believe I attempted finding the v that way, and got the answer wrong. This may have been just a math error on my part, but I wanted to double check.

    I was also curious if that equation is actually need for this problem, or if it's just extraneous information.

    Also, what's the difference between this "propogation velocity" and the maximum velocity of the wave?

    Thanks for the help in advance!
     
    Last edited: Nov 16, 2008
  7. Nov 16, 2008 #6

    Redbelly98

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    It sounds like you just had a math error somewhere, because

    v = λ f

    is the correct formula to use. If you say what you got for λ, f, and v, then we could tell you if that's right or wrong.

    Propagation velocity is the velocity at which the wave or pattern moves along the string. Check out the lower figure here:

    [​IMG]

    The wave pattern just moves along, or propagates, to the right at the propagation velocity.

    I'm not sure what "maximum velocity of the wave" refers to, since in this example the wave moves at a constant velocity. It might really mean the maximum velocity of a point on the string, i.e. the max velocity of the red dot in the above image. But that's just a guess on my part.
     
  8. Nov 16, 2008 #7
    Ok, I'll re-try the formula... Thanks, I probably did just make a mistake. I was just confused why they gave us a forumula.

    There is a reason I'm asking about "Maximum" Velocity being different from this propogation velocity, it's another problem...

    http://img377.imageshack.us/my.php?image=a4physicscn3.png

    Now, problem 12, I figured out no problem.

    But 13 asks for the "maximum transverse velocity", which is NOT the same as the answer to problem 12. This is why I brought this up, as I was now confused what this maximum transverse velocity is. Is that a fancy way of saying the angular frequency here, or is it some other value?

    Thanks for clearing that up with the propogation velocity though. :D
     
  9. Nov 16, 2008 #8

    Redbelly98

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    Ah, okay. The transverse velocity is the velocity of the string itself, for example the red dot in the figures of post #6. "Transverse" means at a right angle to the wave propagation direction; note that the red dot moves up-and-down, at a right angle to the right-going wave propagation direction.
     
  10. Nov 16, 2008 #9
    Ok, so, the difference here is:

    The "propogation velocity" is the speed of the wave going in the x direction

    and the "Transverse Wave Velocity" is the speed of the string going up and down (Y direction)

    That right? Just wanted to make sure, in case I need to explain it to some class mates.

    So, how do I find this transverse wave velocity with the info given? My book doesn't differentiate between the tranverse velocity and the propogation velocity (everything is just v >.>)
     
  11. Nov 16, 2008 #10

    Doc Al

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    OK.

    Careful with terminology. The question asks for "the maximum transverse speed of the particles in the string", which is what you describe. Don't call it the "transverse wave velocity"--that's confusing. (If someone asked me for the "transverse wave velocity", I'd assume that they meant to ask for the velocity of the transverse wave, which is just v.)

    Start with the wave form, which is something like: y = A sin(kx - ωt). That's the y (transverse) coordinate as a function of time and position. Hint: The transverse speed is dy/dt.
     
  12. Nov 16, 2008 #11
    See, that's the thing. My book uses cos as the initial, but other websites use sin. There is a different between teh two functions, despite my professor's claim that they can be both used. I don't believe they can be used interchangably, but that's just me.

    Thank you for correcting my terminology. I figured a derivative was needed, but when I tried it earlier, I got a number much lower then the normal velocity. Now that I know they're different things, I can retry the problem and hopefully get the right result, I'll post here with the fruits of my efforts.

    Thank you again. :D
     
  13. Nov 16, 2008 #12

    Doc Al

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    Your professor is correct; either sine or cosine can be used. Sure they are different functions, but only by a phase factor. (Try it and see!)
     
  14. Nov 16, 2008 #13

    DEW

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    Yep, thats right. Just wanted to join in - too late as usual !!!!
     
  15. Nov 16, 2008 #14
    Ok, I'm having a problem with 11 (the one in my first post).

    I calculated my V = 665.62

    I'm certain this value is right.

    However, there's a problem. The answer I get by plugging in the data, is .014. This answer is wrong.

    I have a stong suspicion that the amplitude for this equation is NOT A0, but another number. As the w is given, and so is the density, the only thing that looks odd is the amplitude.

    So, here's the question: They gave me an x value. Obviously, I need to use it somehow. Is the amplitude A0*e^(-bx)? Cause I tried using that for the amplitude, and got the problem wrong.
     
  16. Nov 16, 2008 #15
    Scratch the question for 13 I asked earlier in this post, I just realized there was a much simpler formula-

    Vmax= w*A

    And that is right. Just need to work on problem 11
     
    Last edited: Nov 16, 2008
  17. Nov 16, 2008 #16

    Doc Al

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    How did you calculate this value?
     
  18. Nov 16, 2008 #17
    I took the K value, and did 2pi/k = 14.61

    Then, I did f = w/2pi = 4.615...

    Whoops, I just made a mistake in my math apparantly, hold on...
     
  19. Nov 16, 2008 #18
    Is the velocity 67.44? And what about my amplitude theory I made before?
     
  20. Nov 16, 2008 #19

    Doc Al

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    That sounds better.
    I agree with what you said earlier:

    That's what I would use. The formula you're plugging into is for a sinusoidal wave; your pulse can be considered a sine wave modulated by that amplitude.
     
  21. Nov 16, 2008 #20
    Thank you, I will try that, give me a bit...
     
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