Simple Harmonic Motion - Physics - Exam Paper, Exams of Physics

Download Simple Harmonic Motion - Physics - Exam Paper and more Exams Physics in PDF only on Docsity! Physics 124 - Analytical Physics SECOND COMMON HOUR EXAM Monday, Apr. 4, 2011 ⇒ ⇐ SIGN HERE NOW: 1. The exam will last from 9:40 - 11:00 p.m. Use a #2 pencil to make entries on the answer sheet. Enter ID information items 2-5, now, on the answer sheet before the exam starts... 2. In the section labeled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 3. Under STUDENT # enter your 9-digit RUID Number. 4. Enter 124 under COURSE; you may ignore the section number. 5. Under CODE enter the exam code given above. 6. During the exam, you may use pencils, a calculator, and one 8.5 x 11 inch sheet (both sides) with formulas and notes. 7. There are 18 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in the answer sheet and this SIGNED cover page. Retain the exam questions attached for future reference and study. 8. When you are asked to open the exam, make sure that your copy contains all 18 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 9. Please have your student ID ready to show to the proctor during the exam. 10. Possibly useful information: at the earth’s surface g = 9.8 m/s2, vsound in air ≈ 340 m/s, ρair ≈ 1.2 kg/m3, the parallel axis theorem is I = Iabout cm +ml2 and I0 = 1×10−12 W/m2 in the dB equation. 1. A 5 kg block attached to a massless spring (constant 20 N/m) undergoes simple harmonic motion with amplitude 0.2 m. At time t = 0 its position is x = 0.0 m and it is moving in the +x direction. Which of the following equations gives x(t) for the block? a) x = 0.2 cos(2t) m b) x = 0.2 cos(t/2) m c) x = 0.2 cos(2t + 0.5) m d) x = 0.2 cos(t/2 + π/2) m e) x = 0.2 cos(2t − π/2) m 2. An object attached to a massless spring undergoes simple harmonic motion of amplitude A along the x axis. At which of the following positions is the kinetic energy of the object twice as large as its potential energy? a) x = A/ √ 3 b) x = A/ √ 2 c) x = A/2 d) x = A/3 e) The kinetic energy is never two times the potential energy. 3. An object undergoes simple harmonic motion of amplitude A, centered at x=0, along the x axis. At which of the following positions can the acceleration be greater than 0 but the velocity be less than 0? a) x = −A b) x = −A/2 c) x = 0 d) x = A/2 e) x = A 4. What is the angular frequency ω of simple harmonic motion of a physical pendulum consisting of a solid disk of mass m and radius r undergoing small oscillations about a point on its edge? It might help to remember that the moment of inertia of this disk about its center of mass is I = mr2/2. a) √ g / r b) √ 2g / (9r) c) √ 2g / (3r) d) √ 2g / r e) √ 4g / r r axis of rotation out of paper movement of disk in plane of paper 13. What is θshock, the angle of the shock wave made by a plane traveling at 3.0 times the speed of sound? a) 70.5◦ = 1.23 radians b) 19.5◦ = 0.340 radians c) 18.4◦ = 0.322 radians d) 39.0◦ = 0.680 radians e) There is no shock wave at that speed. 14. A 1.0 m long string with mass density 1.0×10−2 kg/m is under a tension of 200 N. Both ends of the string are fixed in place. What is the fundamental resonance frequency of the string? a) 340 Hz b) Not enough information is given to determine the fundamental res- onance frequency c) 170 Hz d) 140 Hz e) 70 Hz 15. What length does a long tube with one open and one closed end have to be so that its n=2 harmonic is the same frequency as the n=1 fundamental harmonic of a 0.30 m tube with both ends open? a) 0.45 m b) 0.30 m c) 0.40 m d) 0.23 m e) 0.80 m 16. What is the beat frequency between a 500 Hz source and a 502 Hz source? a) It depends on the speed of sound. b) 0.5 Hz c) 1 Hz d) 2 Hz e) 4 Hz 17. An ant desparately clings to a string along which a sinusoidal wave is trav- eling, so that the ant oscillates back and forth. The wave has an amplitude of 0.02 m, a wavelength of 0.4 m, and a speed of 10 m/s. What is the maximum speed at which the ant moves? a) It cannot be determined from the information given. b) 10 m/s c) 200 m/s d) 3 m/s e) 0.5 m/s 18. Two out-of-phase speakers are positioned 3.5 m apart, both pointing toward a wall 5.0 m in front of them. A listener positioned at the wall, midway between the speakers, hears virtually nothing (destructive interference). Only after moving to one side by 0.84 m does the listener begin to hear a loud sound (constructive interference). What is the frequency of the sound emitted by the speakers? a) 310 Hz b) 620 Hz c) 64 Hz d) 400 Hz e) 200 Hz Physics 124 - Analytical Physics SECOND COMMON HOUR EXAM Monday, Apr. 4, 2011 ⇒ ⇐ SIGN HERE NOW: 1. The exam will last from 9:40 - 11:00 p.m. Use a #2 pencil to make entries on the answer sheet. Enter ID information items 2-5, now, on the answer sheet before the exam starts... 2. In the section labeled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 3. Under STUDENT # enter your 9-digit RUID Number. 4. Enter 124 under COURSE; you may ignore the section number. 5. Under CODE enter the exam code given above. 6. During the exam, you may use pencils, a calculator, and one 8.5 x 11 inch sheet (both sides) with formulas and notes. 7. There are 18 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in the answer sheet and this SIGNED cover page. Retain the exam questions attached for future reference and study. 8. When you are asked to open the exam, make sure that your copy contains all 18 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 9. Please have your student ID ready to show to the proctor during the exam. 10. Possibly useful information: at the earth’s surface g = 9.8 m/s2, vsound in air ≈ 340 m/s, ρair ≈ 1.2 kg/m3, the parallel axis theorem is I = Iabout cm +ml2 and I0 = 1×10−12 W/m2 in the dB equation. 9. What is the fractional change in air pressure from a 1×10−3 W/m2, 100 Hz sound wave? It might help to know that the density of air is about 1.2 kg/m3, the speed of sound in air is about 340 m/s, and that atmospheric pressure is about 1×105 Pa. a) in the range 1×10−3 → 1×10−2 b) in the range 1×10−4 → 1×10−3 c) in the range 1×10−5 → 1×10−4 d) <1×10−5 e) > 1×10−2 10. An object undergoes simple harmonic motion of amplitude A, centered at x=0, along the x axis. At which of the following positions can the acceleration be greater than 0 but the velocity be less than 0? a) x = −A b) x = 0 c) x = −A/2 d) x = A/2 e) x = A 11. Your friend is 5 m from a speaker, and hears a constant 70 dB sound from it. You are 1 m from the speaker. What is the sound intensity at your position? a) 70 dB b) 43750 dB c) 84 dB d) 77 dB e) 1750 dB 12. An ant desparately clings to a string along which a sinusoidal wave is trav- eling, so that the ant oscillates back and forth. The wave has an amplitude of 0.02 m, a wavelength of 0.4 m, and a speed of 10 m/s. What is the maximum speed at which the ant moves? a) 10 m/s b) 0.5 m/s c) It cannot be determined from the information given. d) 200 m/s e) 3 m/s 13. A listener is at x = 0 m moving with velocity +15 m/s x̂. A sound source is at x = −50 m moving with velocity +30 m/s x̂. What is the ratio of the frequency heard to the frequency emitted? It might help to know that the speed of sound in air is about 340 m/s. a) 0.96 b) 0.88 c) 1.05 d) 1.15 e) 1.19 14. A professor demonstrates simple harmonic motion using a wooden block of mass m on a frictionless table attached to a light spring of constant k, oscillating with amplitude A, centered at x=0, along the x-axis. At exactly the moment when the block is at x = −A, the professor accidentally drops a laser pointer onto the block cracking it exactly in half, so that half of it is motionless while the other half continues to undergo simple harmonic motion. The spring is unaffected. What is the ratio of the maximum speed of the full block to the maximum speed of the half block, vmax m/vmax m/2? a) 1 b) 1/2 c) 2 d) √ 2 e) 1/ √ 2 15. A 10 kg mass hangs from a 10-m long vertical rope with mass density 0.10 kg/m. What is the speed of a wave on the rope at the middle of the rope? It might help to know that at the earth’s surface g = 9.8 m/s2. a) 31 m/s b) 33 m/s c) 10 m/s d) 32 m/s e) waves cannot travel in vertical ropes 16. What is θshock, the angle of the shock wave made by a plane traveling at 3.0 times the speed of sound? a) 70.5◦ = 1.23 radians b) There is no shock wave at that speed. c) 39.0◦ = 0.680 radians d) 19.5◦ = 0.340 radians e) 18.4◦ = 0.322 radians 17. What length does a long tube with one open and one closed end have to be so that its n=2 harmonic is the same frequency as the n=1 fundamental harmonic of a 0.30 m tube with both ends open? a) 0.30 m b) 0.45 m c) 0.23 m d) 0.80 m e) 0.40 m 18. What is the angular frequency ω of simple harmonic motion of a physical pendulum consisting of a solid disk of mass m and radius r undergoing small oscillations about a point on its edge? It might help to remember that the moment of inertia of this disk about its center of mass is I = mr2/2. a) √ 2g / (9r) b) √ 2g / r c) √ 2g / (3r) d) √ 4g / r e) √ g / r r axis of rotation out of paper movement of disk in plane of paper 5. A sound wave has intensity 2×10−2 W/m2. How loud is the sound, in dB? It might help to know that I0 = 1×10−12 W/m2. a) -100 dB b) -17 dB c) 103 dB d) 100 dB e) Cannot be determined without knowing the sound frequency. 6. What is θshock, the angle of the shock wave made by a plane traveling at 3.0 times the speed of sound? a) 18.4◦ = 0.322 radians b) There is no shock wave at that speed. c) 19.5◦ = 0.340 radians d) 39.0◦ = 0.680 radians e) 70.5◦ = 1.23 radians 7. A rope has mass density 0.02 kg/m. A sinusoidal traveling wave on it has amplitude 0.05 m, angular frequency ω = 40 radians/s, and speed 12 m/s. What is the power transported by the wave? Note that 1 mW = 10−3 W. a) < 1 mW b) in the range 10 - 100 mW c) in the range 100 mW - 1 W d) > 1 W e) in the range 1 - 10 mW 8. An object attached to a massless spring undergoes simple harmonic motion of amplitude A along the x axis. At which of the following positions is the kinetic energy of the object twice as large as its potential energy? a) x = A/ √ 2 b) x = A/3 c) x = A/2 d) The kinetic energy is never two times the potential energy. e) x = A/ √ 3 9. Two out-of-phase speakers are positioned 3.5 m apart, both pointing toward a wall 5.0 m in front of them. A listener positioned at the wall, midway between the speakers, hears virtually nothing (destructive interference). Only after moving to one side by 0.84 m does the listener begin to hear a loud sound (constructive interference). What is the frequency of the sound emitted by the speakers? a) 400 Hz b) 64 Hz c) 310 Hz d) 200 Hz e) 620 Hz 10. What is the fractional change in air pressure from a 1×10−3 W/m2, 100 Hz sound wave? It might help to know that the density of air is about 1.2 kg/m3, the speed of sound in air is about 340 m/s, and that atmospheric pressure is about 1×105 Pa. a) in the range 1×10−5 → 1×10−4 b) > 1×10−2 c) in the range 1×10−3 → 1×10−2 d) in the range 1×10−4 → 1×10−3 e) <1×10−5 11. A 1.0 m long string with mass density 1.0×10−2 kg/m is under a tension of 200 N. Both ends of the string are fixed in place. What is the fundamental resonance frequency of the string? a) Not enough information is given to determine the fundamental res- onance frequency b) 340 Hz c) 140 Hz d) 170 Hz e) 70 Hz 12. A 10 kg mass hangs from a 10-m long vertical rope with mass density 0.10 kg/m. What is the speed of a wave on the rope at the middle of the rope? It might help to know that at the earth’s surface g = 9.8 m/s2. a) 10 m/s b) 31 m/s c) waves cannot travel in vertical ropes d) 32 m/s e) 33 m/s 13. An object undergoes simple harmonic motion of amplitude A, centered at x=0, along the x axis. At which of the following positions can the acceleration be greater than 0 but the velocity be less than 0? a) x = −A b) x = A c) x = A/2 d) x = −A/2 e) x = 0 14. A professor demonstrates simple harmonic motion using a wooden block of mass m on a frictionless table attached to a light spring of constant k, oscillating with amplitude A, centered at x=0, along the x-axis. At exactly the moment when the block is at x = −A, the professor accidentally drops a laser pointer onto the block cracking it exactly in half, so that half of it is motionless while the other half continues to undergo simple harmonic motion. The spring is unaffected. What is the ratio of the maximum speed of the full block to the maximum speed of the half block, vmax m/vmax m/2? a) 1 b) 1/2 c) √ 2 d) 2 e) 1/ √ 2 1. What is the beat frequency between a 500 Hz source and a 502 Hz source? a) 0.5 Hz b) It depends on the speed of sound. c) 4 Hz d) 1 Hz e) 2 Hz 2. An object undergoes simple harmonic motion of amplitude A, centered at x=0, along the x axis. At which of the following positions can the acceleration be greater than 0 but the velocity be less than 0? a) x = −A b) x = −A/2 c) x = 0 d) x = A/2 e) x = A 3. An object attached to a massless spring undergoes simple harmonic motion of amplitude A along the x axis. At which of the following positions is the kinetic energy of the object twice as large as its potential energy? a) x = A/3 b) x = A/ √ 2 c) x = A/ √ 3 d) x = A/2 e) The kinetic energy is never two times the potential energy. 4. What is θshock, the angle of the shock wave made by a plane traveling at 3.0 times the speed of sound? a) 70.5◦ = 1.23 radians b) 18.4◦ = 0.322 radians c) There is no shock wave at that speed. d) 19.5◦ = 0.340 radians e) 39.0◦ = 0.680 radians 5. A rope has mass density 0.02 kg/m. A sinusoidal traveling wave on it has amplitude 0.05 m, angular frequency ω = 40 radians/s, and speed 12 m/s. What is the power transported by the wave? Note that 1 mW = 10−3 W. a) > 1 W b) in the range 1 - 10 mW c) in the range 10 - 100 mW d) in the range 100 mW - 1 W e) < 1 mW 6. An ant desparately clings to a string along which a sinusoidal wave is trav- eling, so that the ant oscillates back and forth. The wave has an amplitude of 0.02 m, a wavelength of 0.4 m, and a speed of 10 m/s. What is the maximum speed at which the ant moves? a) 0.5 m/s b) 3 m/s c) 10 m/s d) 200 m/s e) It cannot be determined from the information given. 7. A listener is at x = 0 m moving with velocity +15 m/s x̂. A sound source is at x = −50 m moving with velocity +30 m/s x̂. What is the ratio of the frequency heard to the frequency emitted? It might help to know that the speed of sound in air is about 340 m/s. a) 1.05 b) 0.96 c) 1.15 d) 1.19 e) 0.88 8. What is the angular frequency ω of simple harmonic motion of a physical pendulum consisting of a solid disk of mass m and radius r undergoing small oscillations about a point on its edge? It might help to remember that the moment of inertia of this disk about its center of mass is I = mr2/2. a) √ 2g / (9r) b) √ g / r c) √ 2g / (3r) d) √ 2g / r e) √ 4g / r r axis of rotation out of paper movement of disk in plane of paper 9. A sound wave has intensity 2×10−2 W/m2. How loud is the sound, in dB? It might help to know that I0 = 1×10−12 W/m2. a) 103 dB b) -100 dB c) Cannot be determined without knowing the sound frequency. d) -17 dB e) 100 dB 10. A 10 kg mass hangs from a 10-m long vertical rope with mass density 0.10 kg/m. What is the speed of a wave on the rope at the middle of the rope? It might help to know that at the earth’s surface g = 9.8 m/s2. a) 10 m/s b) 32 m/s c) waves cannot travel in vertical ropes d) 31 m/s e) 33 m/s 11. Your friend is 5 m from a speaker, and hears a constant 70 dB sound from it. You are 1 m from the speaker. What is the sound intensity at your position? a) 1750 dB b) 70 dB c) 84 dB d) 77 dB e) 43750 dB