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I don't get something about the speed wave equation

  1. Apr 8, 2007 #1
    a. As the wavelength of a wave in a uniform medium increases, its speed will _____.

    a. decrease
    b. increase
    c. remain the same


    The correct answer is c?? I thought that the change in wavelength always incrases the speed of the medium? What does it mean by uniform medium? Can any one of the variables in the equation [tex]v=f*\lambda[/tex] remain constant? Can 2 of the variables remain constant?

    Btw, I got this problem from: http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/waves/u10l2e.html
     
  2. jcsd
  3. Apr 8, 2007 #2
    Here is another associate problem that I'm confused with:

    c. The speed of a wave depends upon (i.e., is causally effected by) ...

    the properties of the medium through which the wave travels
    the wavelength of the wave.
    the frequency of the wave.
    both the wavelength and the frequency of the wave.

    Whenever the medium is the same, the speed of the wave is the same. However, when the medium changes, the speed changes. The speed of these waves were dependent upon the properties of the medium.

    Does that mean you need to use [tex] v = \sqrt \frac{{F_{T}}}{{\mu}}[/tex] to determine the wave speed. When does plugging in numbers for [tex]v=f*\lambda[/tex] not work?

    It also states: The above example illustrates how to use the wave equation to solve mathematical problems. It also illustrates the principle that wave speed is dependent upon medium properties and independent of wave properties. Even though the wave speed is calculated by multiplying wavelength by frequency, an alteration in wavelength does not effect wave speed. Rather, an alteration in wavelength effects the frequency in an inverse manner. A doubling of the wavelength results in a halving of the frequency; yet the wave speed is not changed.

    Please help me clear up this ambiguity! The information given on the website is correct though right? I don't want to be learning false or incorrect stuff!
     
  4. Apr 8, 2007 #3
    yet another: Doubling the frequency will not alter the wave speed. Rather, it will halve the wavelength. Wavelength and frequency are inversely related.

    How come this is so?? I'm confused. Couldn't the doubling a frequency alter the speed but not the wavelength??
     
  5. Apr 8, 2007 #4
    It will remain the same because wavelength and frequency are inversely related, it one goes up, the other gets smaller. What it means by "uniform medium" is that the the thing the waves is moving through is the same. If a wave changes mediums it will change its speed.

    Think about it: if you shorten the wavelength wont a cycle occur more often since the wave is shorter? The equation [tex]v=f*\lambda[/tex] tells us they are related inversely.
     
    Last edited: Apr 8, 2007
  6. Apr 8, 2007 #5
    For the above problem, "uniform medium" implies constant speed

    Another important thing to note is that when a wave changes mediums, its speed changes along with its wavelength. Frequency is held constant during refraction
     
  7. Apr 8, 2007 #6
    So does "uniform medium" involve the material and the length of the medium? I don't get what the medium involves. I know that medium is what the wave travels through like air particles or a string but it does involve length right? Because if it does involve the length, then what you said would make sense to me because give an length [tex]l[/tex] increasing the wave length would decrease the frequency, or the times of cycles that may occur since each cycle takes up more length.

    I get the inverse relation between frequency and wavelength but I just don't get why the velocity can't be affected either. I mean wave length and the velocity have a direct relationship and doubling one means doubling the other right? Mabye I'm confused because I don't quite understand the problem and what it is asking for. Do you always assume that the velocity is constant? I mean you could increase the velocity in a uniform medium by exerting more intial force right?
     
  8. Apr 15, 2007 #7
    Please tell me if my previous post is correct. Thanks
     
  9. Jul 19, 2009 #8
    i would like to ask a question further , that we say in ocean the its just the wave that travels not the water molecules , then why does water splashes on us on a beach ???
     
  10. Jul 19, 2009 #9
    what is the nature of the wave on the surface of the water ,and the wave travelling inside the surfacce of water ? is it longitudnal or tanslational ??
    how will my answer change if i assume the water is an ideal fluid and there is no viscosity ?
    if the property of surface tension were to be removed , what will be the nature of the wave travelling on the surface of water ?
     
  11. Jul 20, 2009 #10

    Redbelly98

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    Individual water drops or molecules do move, but they only move a short distance back-and-forth and up-and-down. However, the wave can travel for miles and miles ... but the water itself does not move that far.

    It is the short distance that the water moves that causes it to splash on the beach.
     
  12. Jul 20, 2009 #11

    djeitnstine

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    Gold Member

    1) on the surface of the water the molecules of a wave only oscillate up and down. (Imagine "the wave" made in a stadium)

    2) Just under the surface of the wave the molecules form an elliptical pattern about the (up and down, left and right)...however far enough below the surface the molecules only move in a longitudinal pattern.

    *Note this model applies to simple waves not ones such as tsunamis which display a more complicated behavior.

    3) I can't think up a wave model with 0 viscosity at the moment, although I suspect the wave would just maintain its original form forever since there would be no shear forces acting against each molecule.

    4)Surface tension is the microscopic force that attracts each molecule to the other, so if that were gone I would imagine there would be no wave to speak of.

    Correct me if I am wrong on any of them
     
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