Unformatted text preview: Physics 2750 FS 2007 Exam 5 Last Name______________________________ First Name_____________________________ ID # ___________________ This is a closed book exam. I understand, pursuant to University Regulations on academic honesty, that I am not to use any notes or information other than what is in the official, non‐annotated formula sheet. Signature_______________________________________ For multiple choice questions, please make sure that you circle the letter for the answer which you believe to be correct and only that answer. If more than one answer is circled for the same problem, you will not receive credit for it. Don’t get hung up on questions. They should take only one or two minutes each. If you find yourself spending more than a few minutes on a multiple choice question you are probably looking at it the wrong way. You should skip it for now and come back to it later. For full credit show your work for solutions to questions that require calculations. Explain from where you start to solve the problem and show your math flowing from it for full credit. No shown work, no credit! Relax, read carefully, think – and then read everything again. During the exam, if you have questions please raise your hand and the TA or the instructor will come to you and provide help. Consider the graph shown for the position of a ball attached to a spring as it oscillates in simple harmonic motion and use it to answer questions 1 through 3: 1. At which of the following times does the ball have its greatest speed? a) 1 s b) 2 s c) 4 s d) 6 s e) Both 2 and 6 s. 2. At which of the following times does the ball have its greatest acceleration? a) 1 s b) 2 s c) 4 s d) 6 s e) Both 2 and 6 s. 3. At which of the following times is the ball at its equilibrium position? a) 0 s b) 2 s c) 4 s d) 0 and 4 s e) 0, 4, and 8 s 4. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is A. At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = A, the kinetic and potential energies are: a) K = 5 J and U = 3 J b) K = 5 J and U = –3 J c) K = 8 J and U = 0 d) K = 0 and U = 8 J e) K = 0 and U = –8 J 5. What occurs when a wave traveling along a taut string reaches a fixed end where it has been tied to a wall? a) The wave reflects back with the same amplitude, but with opposite sign. b) The wave reflects back with the same amplitude and sign. c) The wave is absorbed by the wall. d) The wave reflects back with smaller amplitude and same sign. e) The wave reflects back with larger amplitude, but with opposite sign. 6. Astronomers can determine the velocity of a galaxy relative to the Earth by observing the light waves emitted by certain elements. If the light frequency from hydrogen atoms is shifted toward a lower frequency as compared to the light emitted from hydrogen atoms on Earth, which one of the following statements correctly describes the velocity of the galaxy? a) The galaxy is moving away from the Earth. b) The galaxy is moving toward the Earth. c) The galaxy is moving along a direction that is perpendicular to the line connecting the Earth and the galaxy. d) The galaxy is not moving relative to the Earth. e) There is too little information given to determine the direction of the velocity of the galaxy. 7. A string of mass m and length L that is fixed at both ends has a fundamental frequency f. A second string of the same linear mass density and under the same tension, which is also fixed at both ends, has a fundamental frequency of 1.5f. The length of the second string is: d) 3L/2 a) L/3 b) 2L/3 c) 4L/9 The drawings show standing waves of sound in six organ pipes of the same length. Each pipe has one end open and the other end closed. Use this figure to answer the next two questions: 8. Some of the drawings show situations that are not 9. Which one of these tubes emits a sound with the lowest frequency? possible. Which one(s) is(are) not possible? a) 1 a) 4 only b) 2 b) 1 and 4 c) 3 c) 5 and 6 d) 4 d) 2 and 3 e) 6 e) 4 and 5 10. What will you most likely do during vacation? a) sleep late b) watch a lot of TV c) forget all the physics you learned d) all of the above 11. A block of mass m = 0.5 kg oscillates, starting from x0 = +25 cm and moving with an initial velocity v0 = +50 cm/s, about its equilibrium position with a period of 1.5 s. a) Calculate the angular frequency and the spring constant. (4 points) b) Calculate the amplitude and the initial phase for this motion. (8 points) c) Write the equation for the position of the particle as a function of time using the values obtained above. (3 points) d) Calculate the maximum speed and the maximum acceleration for the block. (4 points) e) What is the first time that the block is at x = 0 and moving to the right? (6 points) 12. A water wave traveling in a straight line on a lake is described by the equation y ( x, t ) = ( 4 ) cos ( 0.9 x + 5t ) where y is the displacement (in cm) perpendicular to the undisturbed surface of the lake. a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor? (3 points) b) What horizontal distance does the wave crest travel in that time? (3 points) c) What is the number of waves per second that pass the fisherman? (3 points) d) How fast does a wave crest travel past the fisherman? (3 points) e) What is the maximum speed of his cork floater as the wave causes it to bob up and down? (4 points) f) What is the maximum acceleration of his cork floater as the wave causes it to bob up and down? (4 points) 13. Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35.0 m/s. A listener is between the two whistles and is moving toward the right with a speed of 15.0 m/s. No wind is blowing. Take the speed of sound to be 344 m/s. a) What is the frequency from A as heard by the listener? (6 points) b) What is the frequency from B as heard by the listener? (6 points) c) What is the beat frequency detected by the listener? (3 points) MC 50/ Q11 25/ Q 12 20/ Q13 15/ Total 110/ Physics 2750 Formula Sheet Exam 5 OSCILLATIONS: Simple Harmonic Motion x(t ) = A cos(ωt + ϕ0 ) v(t ) = −ω A sin(ωt + ϕ0 ) a (t ) = ω 2 A cos(ωt + ϕ0 ) E= 121 212 kA = mv + kx 2 2 2 ω=
T= k m 2π angular frequency 1 T=period; f = frequency f Simple pendulum ω = T = 2π T = 2π L g I Physical pendulum mgd WAVES y ( x, t ) = A cos(kx − ωt ) 2π k= wave number STANDING WAVES y1 ( x, t ) = A cos(kx − ωt ) y2 ( x, t ) = A cos(kx + ωt ) y = y1 + y2 y= 2A
Astanding wave 2π angular frequency ω = 2π f = T v= λ cos ( kx ) cos (ωt ) λ T speed of wave FT vstring = vP = μ speed of wave in string dy speed of particles in medium dt SOUND WAVES I= P sound intensity 4π r 2 β = 10 log I intensity level I0 fbeats = f 2 − f1 Doppler shift equation as presented in lecture flistener = ⎧upper signs when moving toward v ± vlistener f source ⎨ v ∓ vsource ⎩lower signs when moving away or as presented in your textbook v + vlistener flistener = f source {positive direction from listener to source v + vsource ...
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 Spring '10
 Kostzin
 Frequency, TA, simple harmonic motion

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