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    One end of a long wire under tension is moved up and down sending a wave along it. Assume the wire lies along an x axis with the moving end at the origin. The equation giving displacement y, in meters, of points on the wave is:
    (1) y= (.06 m) sin (5 x - 25 t)
    a. From given constants, calculate the value and units of the quantities called for below:
    angular frequency w, period T, wave number k, wavelength L,
    wave speed c, partial derivative dy/dx at t= .17 sec, and the partial derivative dy/dt at x= 2.2 m.
    b. Find the displacement of a point which is 2.0 m from the origin, at time t=.17 sec. .
    c. For a point which is at x1= 2.4 m from the origin, write y(x1, t) with numbers and units for constants, for the SHM of that point, and find the maximum velocity of that point.

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    Solution Preview

    Physics statements:
    A. The general equation for a traveling wave is given by:
    (2) y= Y sin (k x - w t)
    B. In the general equation, (2), some auxiliary relationships are:
    (3) k= 2 Pi / L
    (4) w= 2 Pi / T
    (5) dy/dt is the "particle velocity", or the velocity of any point on the wave,
    (6) dy/dx is the slope of the sine wave as a function of x at ...

    Solution Summary

    The expert examines traveling wave equations obtaining information about the waves. The displacement of a point of origins are determined.

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