Marie Cornu, a physicist at the Polytechnic Institute in

Chapter 33, Problem 67

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Marie Cornu, a physicist at the Polytechnic Institute in Paris, invented phasors in about 1880. This problem helps you see their general utility in representing oscillations. Two mechanical vibrations are represented by the expressions y1 5 12.0 sin 4.50t and y2 5 12.0 sin (4.50t 1 70.0) where y1 and y2 are in centimeters and t is in seconds. Find the amplitude and phase constant of the sum of these functions (a) by using a trigonometric identity (as from Appendix B) and (b) by representing the oscillations as phasors. (c) State the result of comparing the answers to parts (a) and (b). (d) Phasors make it equally easy to add traveling waves. Find the amplitude and phase constant of the sum of the three waves represented by y1 5 12.0 sin (15.0x 2 4.50t 1 70.0) y2 5 15.5 sin (15.0x 2 4.50t 2 80.0) y3 5 17.0 sin (15.0x 2 4.50t 1 160) where x, y1, y2, and y3 are in centimeters and t is in seconds.