Two traveling waves are generated on the same taut string. Individually, the two
ID: 1469557 • Letter: T
Question
Two traveling waves are generated on the same taut string. Individually, the two traveling waves can be described by the following two equations: y1(x,t = (1.49 cm) sin(k1x+(0.103 rad/s)t+theta1) y2(x,t)=(4.03 cm) sin(k2x-(5.47rad/s)t+theta2) If both of the above traveling waves exist on the string at the same time, what is the maximum positive displacement that a point on the string can ever have? What are the smallest positive values of the unknown phase constants (in radians) such that the above displacement occurs at the origin (x = 0) at time t = 3.00 s? When two travelling waves come together, the result is a new (and potentially very complicated) waveform. How can you express the new waveform in terms of the original two? The sine function is periodic. By how much must the argument of the sine function change in order for the sine function to repeat itself? Keep the answer to this question in mind when addressing the phase constants.Explanation / Answer
1. Well we very well explain the new waveform in terms of the original two by using the concept of phasors. Since in this particular question both Y1 and Y2 contains the sine function, therefore they are in same phase. So for finding maximum positive displacement due to their combination we can simply add their individual maximum displacements.
2. Yes, the sine function is periodic and its fundamental period is 2 pi. So for the function to repeat itself its argument must change in the integral multiples of 2 pi.
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