EF 152 Exam 2 - Spring, 2017 Page 1 Copy 223 Instructions Do not open the exam until instructed to do so. Do not leave if there is less than 5 minutes to go in the exam. When time is called, immediately stop writing, remain seated, and pass your exam to the center aisle. Working after time is called results in an automatic 10 point deduction. Turn your equation sheets in with your exam. Guidelines Assume 3 significant figures for all given numbers unless otherwise stated Show all of your work no work, no credit Write your final answer in the box provided Include units for all answers Harmonic Motion ω angular frequency A amplitude k stiffness m mass δ phase angle x0 initial displacement v0 initial velocity T period f frequency x(t) = A sin(ωt + δ) = a 1 sin(ωt) + a 2 cos(ωt) v(t) = Aω cos(ωt + δ) = a 1 ω cos(ωt) a 2 ω sin(ωt) a(t) = Aω 2 sin(ωt + δ) = a 1 ω 2 sin(ωt) a 2 ω 2 cos(ωt) ω = k m A = a 1 2 + a 2 2 a 1 = v 0 ω a 2 = x 0 δ = tan 1 ( a 2 a 1 ) T = 2π ω f = 1 T Wave Equation v wave velocity A amplitude k wave number ω angular frequency λ wavelength f frequency ω = 2πf y(x, t) = A cos (kx ωt) v is positive if sign of ω is negative. v = λf k = 2π λ Parallel Axis Theorem I = I CM + mr 2 Pendulums simple: ω = g l physical: ω = mgr I Speed of Sound v = B B Bulk Modulus ρ ρ mass density Speed of Sound in Air: v (331 +.6T)m/s (T in ) v (20.05 T)m/s (T in K) Natural frequencies λ wavelength L Length n harmonic T tension μ mass per unit length f frequency v wave velocity in medium String: λ n = 2L n f n = v λ = n 2L T μ Air Columns: λ = 4L n λ = 2L n closed (n = 1, 3, 5, ) open (n = 1, 2, 3, ) Wave Speed: Cables, Ropes, etc. T Tension μ mass per unit length E Modulus of elasticity ρ mass density Transverse: v = T μ Longitudinal: v = E ρ Sound Level β(in db) = 10 log I I 0 I Intensity I 0 reference intensity, 1 10 12 W/m 2 Doppler Shift f 0 frequency f shifted frequency v velocity of sound in medium v L velocity of listener v S velocity of source f = f 0 v+v L v+v S Beat Frequency: f 1 f 2 + listener to source Wave Energy, Power, Intensity E energy I intensity P power P average power E = 2π 2 μvtf 2 A 2 P = P = 2π 2 μvf 2 A 2 P = 4π 2 μvf 2 A 2 cos 2 (kx ωt) I = P I 2 4πr 2 = r 2 1 I 1 Light Waves Law of Reflection: r 2 2 θ r = θ a Index of refraction: n = c v Snell s Law: n a sin θ a = n b sin θ b Light wavelength: λ = λ 0 n Total Internal Reflection: sin θ crit = n b n a speed of light in vacuum: c = 3 10 8 m/s
EF 152 Exam 2 - Spring, 2017 Page 2 Copy 223 8:10 9:40 11:10 12:40 2:10 3:40 102 216 217 218 A102 Chris R B102 Stefy C102 Stefy D102 Chris H E102 Chris H F102 Chris H A216 Heather B216 Heather C216 Chris R D216 Chris R E216 Stefy F216 Charlie A217 Charlie B217 Thuy C217 Charlie D217 Heather E217 Thuy F217 Thuy A218 Connor B218 Connor C218 Connor D218 Michael E218 Michael F218 Michael
EF 152 Exam 2 - Spring, 2017 Page 3 Copy 223 Name: Section: 1. Write your name and section above. Specify your EXAM ID below. Use 000 if you don t know your exam ID. 0 1 2 3 4 5 6 7 8 9 Digit #1 Digit #2 Digit #3 4. (2 pt) Red light has a wavelength of 700 nm and violet light has a wavelength of 400 nm. Which has the higher frequency? Red Violet Same 5. (2 pt) What remains the same as light travels from water to air? Frequency Velocity Wavelength None of these 6. (2 pt) What is the sound level of a sound at the lower threshold of human hearing? 0 db 1 db -12dB 1x10-12 db 7. (2 pt) You know the total weight and cross-sectional area of a cable. What else do you need to know to calculate µ? Length Diameter Tension Nothing else needed 8. (2 pt) What is the relationship between the velocity of a wave (v w) and the velocity of a particle (v p)on the wave? vw < vp vw = vp vw > vp No relationship 9. (2 pt) Pendulum #1 starts with an offset 5 from vertical. Pendulum #2 is identical to #1 and starts with a 10 offset. How do the frequencies compare? f1 < f2 f1 = f2 f1 > f2
EF 152 Exam 2 - Spring, 2017 Page 4 Copy 223 10. (2 pt) Which term refers to the decaying amplitude of a pendulum due to friction? Damping, regression, phase angle, stiffness Damping Regression Phase Angle Stiffness 11. (2 pt) Where does an object moving in SHM have its maximum speed? x = 0 x = ½ A x = A 12. (2 pt) Where does an object moving in SHM have its maximum acceleration magnitude? x = 0 x = ½ A x = A 13. (2 pt) A wave is defined by the equation 5cos(2π x 2π t). What is the wave velocity? 0 m/s 1 m/s 2π m/s 5 m/s
EF 152 Exam 2 - Spring, 2017 Page 5 Copy 223 14. (5 pt) What is the sound level (in db) 8.2 m away from a 3.0 W speaker? 15. (5 pt) What length of an open-ended pipe will have a 3 rd harmonic with a frequency of 790 Hz? (use v sound = 343 m/s) 16. (5 pt) What is the length of a simple pendulum with a period of 1.25 seconds? 17. (5 pt) What is the time required for sound to travel 1.6km in 5 C air?
EF 152 Exam 2 - Spring, 2017 Page 6 Copy 223 18. (12 pt) Thuy visits an aquarium and points a laser pointer into a tank as shown and the beam hits a blue octopus. She measures the distances as shown. How far away (x) is the octopus? (neglect the thickness of the glass) n air=1.0, n water=1.33 1.6 ft 2.4 ft 3.5 ft x 19. (12 pt) Dr. Kit and his class travel to a newly discovered planet to experimentally determine the acceleration due to gravity. They do this by removing the license plate from their spaceship and swinging it from one of the mounting holes. His class measures the period of oscillation to be exactly 1.4257 seconds. What is value for gravitational acceleration on this planet? I cm of a rectangle = m 12 (b2 + h 2 ) 0.40 ft 0.45 ft 0.18 ft 1.1 ft
EF 152 Exam 2 - Spring, 2017 Page 7 Copy 223 20. (12 pt) Charlie is driving to the dentist at 45 mph. Chris is going in the opposite direction and speeding to the ER at 70 mph. After they pass, Chris honks his horn and Charlie hears a frequency of 521 Hz. What was the actual frequency of Chris horn? (v sound = 767 mph) 21. (12 pt) Dr. B is tuning her fiddle using a 256 Hz tuning fork. She plucks a string and hears a fundamental frequency with slightly higher pitch and a beat frequency of 3 Hz. The string has a mass of 5.0 g and a length of 0.61 m. What is the tension in the string?
EF 152 Exam 2 - Spring, 2017 Page 8 Copy 223 22. (12 pts) Heather hangs a 1.3 kg mass on a spring (k=220n/m). She pulls it down 18 cm below its equilibrium position and releases it with an upward velocity of 4.0 m/s. Where is the mass (relative to the equilibrium position) after 4.0 seconds? Assume ideal motion (no losses).