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Find the distance this spot travels in one period.

  1. May 17, 2006 #1
    Ive been trying this problem for awhile now and I seem to not get it.

    A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 2.5s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1m. The frequency at which the crests pass a given point in space is 0.4 Hz. The distance between the two adjacent crests on the wave is 2m.

    a) There is a blue spot drawn onto the rope with a magic marker. Find the distance this spot travels in one period.

    I have tried using the equation y(t)=Asin(2*pi*f*t)
    which is 0.1m*sin(2*pi*.4*2.5) = .0109 m and I got this wrong. I am not sure where I did go wrong and was wondering if anyone can help me. Thanks.
     
  2. jcsd
  3. May 17, 2006 #2

    nrqed

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    This equation gives the vertical position and since the point is moving up and down, calculating the position will not give the distance travelled. (I could move 20 meters to the right and then come back and my position will not have changed but the distance travelled will be 40 meters).

    You should just visualize it. Let's say that the point is initially at the very top. Then as the wave passes it will move down for a while and eventually start moving up again. In terms of the amplitude A, what distance does it travel in one period?

    Pat
     
  4. May 17, 2006 #3
    crust to crust would be 2m, the one that i calculated, (velocity/frequency)
    and in one period does it travel half the distance of amplitude?
     
  5. May 18, 2006 #4
    .1m x 4 = .4m, i think i get it now
     
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