Mastering Waves and Phasors: Homework Guide and Solutions
School
Brigham Young University, Idaho**We aren't endorsed by this school
Course
ECEN 390
Subject
Electrical Engineering
Date
Dec 12, 2024
Pages
3
Uploaded by ProfessorOpossumMaster1110
Traveling Waves and Phasor Homework (30 Points) (jas, Traveling Waves and Phasor HW.docx, 8/19/2021) Use units and clearly label answers using 3 or 4 significant digits where appropriate. Show your work so that if necessary partial credit can be awarded. 1.Determine the wavelength in meters of a 2 GHz electromagnetic wave traveling through a vacuum, meaning up= c. (2 points.) ?𝑛 ?𝑎𝑝𝑒𝑟2.Determine the wavelength in miles of a 60 Hz electromagnetic wave traveling along a power line at a speed of 70% of the speed of light. (2 points.) On Paper 3.Two waves y1(t) and y2(t) have the same amplitude and frequency, but y2(t) leads y1(t) by 60°. Given y1(t) = cos[2π(1000)t], write the expression for y2(t) in terms of the cosine function using radians for the argument. (3 points.) On Paper 4.The voltage of an electromagnetic wave traveling on a lossy transmission line is given as follows where z is the distance in meters from the source: v(z, t) = 5e−αzsin[(4π x 109)t − 20πz].a.Find the frequency in Hz, wavelength in meters (m), and phase velocity of 𝐯(𝐳, 𝐭) in meters per second (m/s). (2 points each for 6 points total for part a.) On Paper b.Find αGiven that the wave envelope equals 1.5 V for z = 2 meters. (2 points) On Paper
5.Find the phasor representations of the following time functions. Simplify your results to be of the form rejθrwith r being a positive quantity and θrIn radians. (15 points total.) a.v(t) = 9cos(ωt –π/3) V. (2 points.) On Paper b.v(t) = 12sin(ωt+ π/4) V. (2 points.) On Paper c.i(x, t) = 5e−3xsin(ωt + π/6) A. (3 points.) On Paper d.i(t) = −2cos(ωt + 3π/4) A. (4 points.) On Paper e.i(t) = 4sin(ωt + π/3) + 3cos(ωt - π/6) A. (4 points.) On Paper