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Maximum speed of a string help

  1. Nov 29, 2008 #1
    maximum speed of a string...help plz

    A tranverse mechanical wave is traveling along a string lying along the x axis. The displacement of the string as function of position and time, y(x,t) is described by the following equiation:

    y(x,t)=0.044 sin(4.20x-152t) where x and y are in meters and t is in secnds. Find the wavelength of the wave, the velocity of the wave and the maximum speed in the y direction of any piece of the string.

    i have done yet the wavelength and the velocity but i dont know how to calculta the maximum speed in the y direction o any piece of the string.

    wavelength= 1.50 meter
    velocity of wave= 32.3 m/s
    maximum speed= "I don't know"

    can anyone help me plz
     
  2. jcsd
  3. Nov 29, 2008 #2
    Re: maximum speed of a string...help plz

    Here are a few pointers:

    1) Generally, v= ds/dt, so, what do you need to do with the wavefunction?
    2) Where and when does a particle on a wave achieve maximum transverse (in the y direction) velocity ?
     
  4. Nov 29, 2008 #3
    Re: maximum speed of a string...help plz

    do yoy mean derivate the y equation?.... and set x = o
     
  5. Nov 29, 2008 #4
    Re: maximum speed of a string...help plz

    Yes, precisely. There is a simpler method for the 2nd part, however. What is the maximum value of the trig function that you'll find in the derivative?
     
  6. Nov 29, 2008 #5
    Re: maximum speed of a string...help plz

    y=0.044 sin(4.20x-152t)

    dy/dt= 0.044cos(4.20x-152t)(152)

    and then set x=0

    is this correct?....
     
  7. Nov 29, 2008 #6
    Re: maximum speed of a string...help plz

    not exactly right, what is the maximum value [cos (4.20x-152t)] can take? (Hint: cos(f(x)) has a finite range between ... and ...)
     
  8. Nov 29, 2008 #7
    Re: maximum speed of a string...help plz

    i really dont know because in the equation i have a t for time yet, so what i do with that variable?... or what i have to set in the derivate for get the maximum speed?...
     
  9. Nov 29, 2008 #8
    Re: maximum speed of a string...help plz

    well, the simple answer is that the maximum value of a cos function is always 1, regardless of the variable present within the function (assuming, of course, that their domains are for all real numbers). For max speed, the cos (4.20x-152t) simply equals 1.
     
  10. Nov 29, 2008 #9
    Re: maximum speed of a string...help plz

    oh yes i foget that in an instant so my

    y=0.044 sin(4.20x-152t)

    dy/dt= 0.044cos(4.20x-152t)(152)

    so the max speed is (0.044))(152)

    is this now right?.... do i derivate correctly?....
     
  11. Nov 29, 2008 #10
    Re: maximum speed of a string...help plz

    Yes, that should be right.
     
  12. Nov 30, 2008 #11
    Re: maximum speed of a string...help plz

    thanks... it is the correct answer
     
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