Explore BrainMass

Explore BrainMass

    Calculate the derivatives of wave equations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t)
    To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t.

    a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave.

    A separate wave on the same wire is: (3) y= 0.5 sin (6x + 4t)

    b. For y= 0.5, solve for x to get (4) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave.

    c. From parts a and b, state how you can tell whether a wave is moving toward +x or toward -x direction.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:12 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/calculate-derivatives-wave-equations-7205

    Solution Preview

    a. In a general equation, y= ym sin (kx - wt), if we let y= ym then ym cancels and we get:
    sin (kx - wt) = 1 from which kx - wt = Arcsin 1 and x= (w/k)t + (Pi)/(2k)
    In ...

    Solution Summary

    The derivatives of wave equations are determined. A separate wave on the same wire are determined. With good explanations and calculations, the problems are solved.

    $2.19

    ADVERTISEMENT