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A wave is generated and moves along a taut wire: amplitude, velocity and wavelength

See attached file.

One end of a taut wire moved up and down with SHM generates a wave moving to the right along the wire. A 'primed' axis system, (x', y'), moving along with the wave, gives the x',y' coordinates of points on the wave as shown in ATTACHMENT #1.
The wave's amplitude is ym', its velocity is v, and its wavelength is (lambda).

ATTACHMENT #1 also shows a stationary axis system, x,y superimposed on the x',y' system. Any point on the wave has x,y coordinates and also x', y' coordinates.
We wish to express the traveling wave in terms of x and y coordinates.

PART a. Develop y as a function of x, and time t, in terms of its constants ym and angular frequency (omega), then SEE ATTACHMENT #2 to check your work.

PART b. If the crests of the wave are 1.6 m apart, the amplitude is .02 m, and the period is .47 sec, find the value of y at a point which is 2.4 meters from the x,y origin at time t= .55 sec.

PART c. Find the difference in phase between two points on the wire which are .25 meters apart.

Attachments

Solution Preview

See attached file.

PART a.
The equation called for, (6), involves three variables, y, x, and t, and three constants, ym , k, and (omega). Auxiliary ...

Solution Summary

The solutions are explained and the workings are included.

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