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Wave functions and dynamic question

  1. Jun 28, 2011 #1
    1. The problem statement, all variables and given/known data

    The displacement from equilibrium caused by a wave on a string is given by
    y(x, t) = (−0.00217 m)sin[(44.4 m−1)x − (728 s−1)t].

    i need to find

    (b) number of waves in 1 m
    waves

    (c) number of complete cycles in 1 s
    cycles

    (d) wavelength


    (e) frequency


    3. The attempt at a solution

    i first thought the wavelenght was 44.4m because of the formula
    Acos2pi(x/λ - t/T)

    but then i realized that you had to use the other formula : Acos(kx - wt)

    so k = 1/44.4m = 2pi / λ

    so λ wave length is 278.97m ?? is this right?

    then w = 2pif = 1/728s

    so f = 2.186 * 10 ^-4 HZ

    and with λ and f you can find the Velocity

    not sure if i found λ and f right? can you please tell me if i did it right?

    b) number of waves in 1 m
    i'm guessing you find this by 1/λ

    (c) number of complete cycles in 1 s
    and you find this by doing 1/ T

    i just want to make sure this is right. if the λ and f are right so i can get the rest of the answer

    thank you!
     
  2. jcsd
  3. Jun 28, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The units look weird. Instead of m-1 use m-1 or 1/m. The same for s-1.
    So the wave is y(x,t)=(−0.00217 m) sin[(44.4 m−1)x − (728 s−1)t].

    No, k=44.4 m-1. Otherwise your way of solving the problem will be correct.

    ehild
     
  4. Jun 28, 2011 #3
    so k =44.4m^-1

    does that equal to k = 1/44.4m what does m^-1 mean?
     
  5. Jun 28, 2011 #4

    ideasrule

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    Homework Helper

    No, because k=1/44.4m is the same as 1/44.4 m^-1, which is 0.0225 m^-1. k is proportional to the inverse of the wavelength and wavelength is measured in m, so you'd expect the units to be m^-1.
     
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