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.
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 ...