Physics 2C, Fall 2014 Coach: Ken Intriligator Quiz 2, Version D Oct 17, 2014 Instructions A. Write your name and student ID number at the top of this sheet. You must show all work here, and turn this in with your scantron. B. Academic Integrity Announcement: I understand that cheating is an academic FELONY, which is taken very seriously by UCSD. Punishment includes an F grade in the class, and possible suspension or expulsion from the University. I understand that the TA and proctors have the right to randomly check my ID, and that it is their duty to report any suspicious activity. I understand that I will turn in this exam, and that it will be kept as a record of my work. There will be both random and non-random integrity checks. I understand that many methods will be used to detect cheating. I understand that enabling another student to copy my answers is also considered cheating, with the same consequences. YES, I UNDERSTAND, AND WILL OF COURSE FOLLOW THE UNIVERSITY’S RULES ABOUT ACADEMIC INTEGRITY (NO CHEATING). PLEASE SIGN: C. No calculators or electronic devices. Approximate π ≈ 3. Other possibly useful approximate facts: 1atm ≈ 105 P a, ρH2 O ≈ 103 kg/m3 , g = 9.8m/s2 ≈ 10m/s2 . 1 INTENTIONALLY LEFT BLANK. USE THIS SIDE FOR ANY OF YOUR ADDITIONAL CALCULATIONS. 2 1. A traveling wave is moving to the left on a string, in the negative x direction, with a speed of 6m/s. Which answer below can represent the wave’s transverse displacement of the string? (The units are not written here explicitly – just imagine that everything has appropriate units of meters, kilograms, and seconds.) (a) (b) (c) (d) (e) y(x, t) = 3 cos(3x + 2t) y(x, t) = 2 sin(10x + 60t) 4 y(x, t) = 10 cos(3x − 2t) y(x, t) = 36 cos(6x + t) y(x, t) = 6 sin(2x − 12t) 2. A traveling wave on a string has an average power of 100W . What would be the average power of a traveling wave (on the same string) with three times the original amplitude and one-half of the original period? (a) (b) (c) (d) (e) 600W 60W 6000W 400W 3600W 4 3. A traveling wave is moving on a long string (which stretches along the x-axis). The wave is transverse (displacement along the y axis) and moves along the x axis with velocity 10m/s, with amplitude 0.3 meters, and a wavelength of π meters. What is the maximum transverse velocity vy of the string? (a) (b) (c) (d) (e) 10m/s 20m/s 3m/s 30m/s 6m/s 4 4. Suppose that we combine a left-moving traveling wave with amplitude A and a right-moving traveling wave with amplitude A. Both waves have the same wavelength, and both satisfy y(0, 0) = 0. The combination (sum) is (a) (b) (c) (d) (e) A standing wave with amplitude 2A 4 A traveling wave with amplitude 2A A standing wave with amplitude A Another traveling wave, with amplitude A Not a solution of the wave equation 5. Your pet ant Klyde really loves riding traveling sine waves on your stretched rope! For the first ride, you set up the wavelength and amplitude such that Klyde’s maximum acceleration (while he holds on to the rope) is g. For his second ride, Klyde begs you to increase the amplitude by a factor of 5, A2 = 5A1 , but to keep the wavelength and maximum acceleration the same as for his first ride. What tension do you need for ride 2? (a) (b) (c) (d) (e) τ2 τ2 τ2 τ2 τ2 =√ (1/5)τ1 4 = 5τ1 = τ1 = 5τ1 √ = τ1 / 5 3 6. A string of length 3 meters, and mass 3kg, has both ends fixed (tied down). There is a standing wave on the string, which has nodes (places of zero displacement) at x = 0, x = 1, x = 2m, and x = 3 meters. (You might want to draw the wave for yourself to see the picture.) The wave oscillates with a period of 0.5 seconds. What is the tension of the string? (a) (b) (c) (d) (e) 2N 9N 3N 16N 4 4N 7. A string of length 3m has both ends fixed (tied down). There is a standing wave on the string. Which of the following is correct? (a) (b) (c) (d) (e) The largest possible wavelength is 3m There is no minimum or maximum possible wavelength The largest possible wavelength is 6m 4 The smallest possible wavelength is 3m The smallest possible wavelength is 6m 8. Suppose that a 5 meter long length of string has a mass of 1kg and a tension of 3N . There is a wave on the string such that, at some time t0 , and position x0 , the displacement has ∂ 2 y/∂x2 = 2m−1 . What is the transverse acceleration of the string at that time t0 and position x0 ? (a) (b) (c) (d) (e) 10m/s2 30m/s2 4 150m/s2 15m/s2 6m/s2 Good luck! 4