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How to find wave oscillations?

  1. Mar 29, 2015 #1
    1. The problem statement, all variables and given/known data
    A wave has a wavelength of 3.0m; a frequency of 25.0 Hz; and amplitude of 14.0 cm. The wave travels in the positive x-direction and has a value of zero at t=x=0. How many complete oscillations has the wave made at t= 20.0 s and x=4.2 m?

    A) 3132
    B) 1566
    C) 498
    D) 25
    E) 3

    2. Relevant equations
    T=1/f

    3. The attempt at a solution
    Looking at the problem I was confused because if the wave length is 3m and the x distance after it stops is 4.2 meters, wouldn't it only complete one full oscillation?
     
  2. jcsd
  3. Mar 29, 2015 #2

    ehild

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    You have to consider the phase of the wave, how many times 2pi is it.
     
  4. Mar 29, 2015 #3
    what do you mean? what is the phase of the wave?
     
  5. Mar 29, 2015 #4

    NascentOxygen

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    How many cycles are produced during that 20 second duration?
     
  6. Mar 29, 2015 #5
    that would be the frequency times the time period? so 25×20?
     
  7. Mar 29, 2015 #6

    ehild

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    You write the wave as y=Asin(ωt-kx). The argument of the sine is the phase.
     
  8. Mar 29, 2015 #7

    NascentOxygen

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    So in 20 seconds, 25x20 cycles propagate outwards from the origin.
     
  9. Mar 29, 2015 #8
    So 500 would be the answer?
     
  10. Mar 29, 2015 #9

    NascentOxygen

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    The answer to which question, exactly?
     
  11. Mar 29, 2015 #10
    the original equation: How many complete oscillations has the wave made at t= 20.0 s and x=4.2 m?
     
  12. Mar 29, 2015 #11

    NascentOxygen

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    I can see how the 20 seconds is accounted for, but where have you taken into consideration that 4.2 meters?
     
  13. Mar 29, 2015 #12
    thats what im confused about
     
  14. Mar 29, 2015 #13
    I don't understand how the two go together?
     
  15. Mar 29, 2015 #14

    NascentOxygen

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    That 4.2m is your monitoring distance from the origin. The origin is the point where the waveform propagates from.
     
  16. Mar 29, 2015 #15
    so how does it affect the 20×25?
     
  17. Mar 29, 2015 #16

    NascentOxygen

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    You need to draw a diagram. A set of axes, with the wave originating at the origin and moving out along the x axis. Mark on it the 4.2 m.
     
  18. Mar 29, 2015 #17
    How will that help me?
     
  19. Mar 30, 2015 #18

    andrevdh

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    We can see from the problem that you are at the point in the course where you need to acquire this knowledge
    This simulation might help, although here the wave is reflected back at the right hand end (select loose end ,oscillate and no damping):
    https://phet.colorado.edu/en/simulation/wave-on-a-string
     
    Last edited: Mar 30, 2015
  20. Mar 30, 2015 #19

    ehild

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    You might consider to follow my method shown in Post #6 .

    The wave is a function of both t (elapsed time) and x ( the distance travelled ) .
    It can be written as y=A sin(ωt-kx) where ω is the angular frequency and k is the wavenumber. In terms of frequency f and wavelength λ, the wave is y=Asin[2π(f t - x/λ) ].
    y = 0 when x = 0 and t = 0. A complete oscillation means that the phase 2π(f t - x/λ) changes by 2π and y returns to zero. You have to calculate how many times it happens till the given time and distance.
     
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