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From a traveling wave equation obtain much information about the wave.

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.

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 ...

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