1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Transvese Velocity of a Standing Wave

  1. Jan 28, 2015 #1
    λ∂1. The problem statement, all variables and given/known data
    Aguitar string lies along the x-axis when in equilibrium. The end of
    the string at x=0 (the bridge of the guitar) is fixed. A sinusoidal
    wave with amplitude A=0.750 mm and frequency
    f =440 Hz, corresponding to the red curves in Fig. 15.24,
    travels along the string in the -x-direction at 143m/s. It is reflected
    from the fixed end, and the superposition of the incident and reflected
    waves forms a standing wave. (a) Find the equation giving the displacement
    of a point on the string as a function of position and time.
    (b) Locate the nodes. (c) Find the amplitude of the standing wave and
    the maximum transverse velocity and acceleration.


    2. Relevant equations
    ∂y(x,t)/∂t=AswSin(kx)Cos(wt)w
    T=1/f
    λ=v/f
    position of a node=λ/2

    3. The attempt at a solution
    So, I get how to do everything up until part c.

    The partial derivative of the transverse wave with respect to time and holding x constant is:

    ∂y(x,t)/∂t=(4.15/m/s)sin[(19.3 rad/m)x]cos[(2760rad/sec)t

    Now, by just looking at this function, I could tell that the maximum velocity is 4.15. The function will oscillate between +4.15 and -4.15.

    Well, I thought that if I find the position of a node and the time at which it will occur, this function would yield to an answer of 4.15m/s.

    The values I used for the period is .002sec so, a node will happen at half a period which is .001sec.
    One wavelength is .325m and a node will happen half way through. This means that a node will occur at x=.1625m.

    When I plug in the values in the above equation I get -.020599061m/s which is not the correct an answer. Would you please let me know if I am thinking about this incorrectly? Doesn't maximum velocity happen at the intersection point with the x-axis? Isn't this point a node in this case? This is an example in a textbook and I am trying to figure the maximum velocity by not just looking at the amplitude of the function.
     
  2. jcsd
  3. Jan 28, 2015 #2

    dlgoff

    User Avatar
    Science Advisor
    Gold Member

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Transvese Velocity of a Standing Wave
Loading...