Chapter 15, example problems:


 Ralf Roberts
 2 years ago
 Views:
Transcription
1 Chapter, example problems: (.0) Ultrasound imaging. (Frequenc > 0,000 Hz) v = 00 m/s. λ <.0 mm. Frequenc required > 00 m/s /.0 mm = Hz. (Smaller wave length implies larger frequenc, since their product, being equal to the sound velocit, can not change. (.) Speed of propagation vs. particle speed. Eq. (.): (x, t) = A cos[ω (x/v t)] = A cos [πf (x/v t)]. (a) Putting in ω = v k, k = π / λ, and using the fact that v (x/v t) = (x v t), we obtain: (x, t) = A cos[( π / λ) (x v t)]. (b) The transverse velocit of a particle in the string on which the wave travels: The transverse displacement of a particle at position x on that string as a function of t is (x, t) = A cos[( π / λ) (x v t)], so the transverse velocit of that particle as a function of t is: v (x, t) = {A cos[( π / λ) (x v t)] } / t x = A sin[( π / λ) (x v t)] ( π / λ) ( v) = ( π f) Α sin[( π / λ) (x v t)]. (c) The maximum transverse speed of a particle in the string, v max, is just the amplitude of the above velocit wave, namel π f Α (= ω Α). (This is the same expression as that for the maximum velocit of a harmonic oscillator. This is not a coincidence. Ever point in a wave is indeed executing a simple harmonic motion, onl with a phase which varies with x.) This maximum transverse velocit of a particle in the string is in general different from the wave velocit. For them to be equal, we would have to require ω Α = v, or, since ω = v k, we would have to require kα =, which just means Α = λ / π. For this maximum transverse velocit to be less or greater than the wave velocit, wee need A to be less or greater than λ / π. (In realit, A is practicall alwas much less than λ / π. Thus the maximum transverse velocit of a particle in the string is practicall alwas much less than the wave velocit.) (.6).0 m string, weight. N. Tied to the ceiling. Lower end supports a weight W. Plucked slightl. Wave traveling up the string obes: (x, t) = (8.0 mm) cos(7 m x 70 s t)] (thus x is measured upward). (a) Time for a pulse to travel the full length of the string: We need the wave velocit, which is 70 s / 7 m =.87 m/s. Then the travel time is.0 m /.87 m/s = 0.09 s. (b) Actuall, this problem is correct onl if the weight of the string,. N, is much less than the weight W, and therefore can be neglected with respect to the latter. Then the tension in the string, F, is due to W alone, and is therefore equal to W. The linear mass densit of the string, μ, is (. N / 9.8 m/s ) /.0 m = kg/m. Then using the formula for the velocit of a transverse wave on a string, v = (F / μ), we can find W = v μ = (.87 m/s) kg/m =. N, which is indeed much larger than. N, confirming the validit of the approximation we made in the beginning. (But the error is about %.)
2 (c) The number of wavelengths on the string at an instant of time =.0 m / (π / 7 m ) =.. (d) Equation for waves traveling down the string is: (x, t) = A cos [( π / λ) (x m/s t)]. (That is, A and λ can be different for different waves, but the velocit of the waves must all be the same 87. m/s, since it is determined b the tension and the linear mass densit of the string.) (.) Threshold of pain. Intensit of sound is 0. W/m at 7. m from a point source. At what distance from the point source will intensit reach the threshold of pain,.0 W/m? Denote the new distance D. Then.0 W/m πd = 0. W/m π (7. m) = power output of the point source. Hence D = 7. m (0. W/m /.0 W/m ) / =.87 m. (Note: πd is the area of a sphere of radius D.) Thus ou have to move 7. m .87 m =.0 m toward the source of sound to reach the threshold of sound. (.8) Interference of triangular pulses. v =.00 cm/s..00 cm.00 cm.00 cm.00 cm.00 cm.00 cm.00 cm.00 cm/s 0. s = 0. cm. The two pulses will barel touch after traveling for 0. s, producing:.00 cm.00 cm.00 cm.00 cm.00 cm.00 cm.00 cm/s 0.0 s =.0 cm. The two pulses now overlapped b.00 cm..00 cm.00 cm The superposed pulses now show a flat top for a width of.00 cm.
3 .00 cm/s 0.7 s =. cm. The two pulses now totall overlap. Their superposition gives one triangular pulse of twice the height, but the same old width of.00 cm. But this shape is maintained for onl one instant of time, since part of it is moving to the right, and part of it is moving to the left..00 cm.00 cm.0 cm.00 cm.00 cm.0 cm.00 cm/s.00 s =.00 cm. The two pulses have now moved pass each other b.0 cm. The superposition again produces the trapezoidal shape with a flat top of.00 cm just like when it has onl moved for 0. s. But notice the directions of the two horizontal arrows, which indicate the directions of motion of the two constituent pulses..00 cm.00 cm.00 cm/s. s =.0 cm. The two pulses have now moved pass each other b their own width, so the no longer overlap. The situation appears just like when the have moved for onl 0. s, except for the directions of the two horizontal arrows, which indicate the directions of motion of the two constituent pulses..00 cm.00 cm.00 cm.00 cm.00 cm.00 cm
4 (.) Distance between adjacent antinodes of a standing wave is.0 cm. A particle at an antinode oscillates in SHM with amplitude 0.80 cm and period s. The string is along x and is fixed at x = 0. (a) Adjacent nodes are also.0 cm apart. (b) Recall that cos (A B) + cos (A + B) = cos A cos B, which implies that A cos (kx ωt) + A cos (kx + ωt) = A cos (kx) cos (ωt). Hence the amplitude of a standing wave is a factor two larger than the amplitude of either of the two constituent traveling waves, but their wavelengths are the same, and their frequencies are the same. Thus: Wavelength of each traveling wave λ = 0.0 cm; Amplitude of each traveling wave A = 0. cm. Speed of each traveling wave v = λ f = λ / Τ = 0.0 cm / 0.07 s = 00 cm/s = m/s. (c) Maximum transverse speed of a point at the antinode of the standing wave = Aω = A (π / T) = 0.80 cm (π / s) = 7. cm/s. Minimum speed = 0. (d) Shortest distance bweteena node and an antinode is 7.0 cm. (.) Weightless ant. An ant of mass m stands on top of a horizontal stretched rope. Rope has mass per unit length μ and tension F. A sinusoidal transverse wave of wave length λ propagates on the rope. Motion is in the vertical plane. Find the minimum wave amplitude which will make the ant momentaril weightless. The mass m is so small that it will not affect the propagating wave. The ant will becomes momentaril weightless when it momentaril needs no support from the rope. This happens when its mass times the maximum downward acceleration of the SHM of the ant is exactl equal to its weight. This happens when the ant is at the highest point of its SHM. [Then just before or after this moment, the acceleration will still be downward but with a magnitude less than this maximum value, and the weight of the ant will need to be partiall cancelled b an upward support force from the rope, so that the net downward force is still equal to (now smaller) ma. Thus the weightlessness feeling happens onl at that brief moment when the ant is at the highest point of the SHM. During the half ccle of the motion when the acceleration is pointing upward, the weight is pointing in the wrong direction to provide the needed force. So an upward support force from the rope larger than the weight of the ant will exist, so that the net force is upward, and is still equal to ma. Thus in this half ccle the ant actuall weights more than its actual weight, if ou put a scale between the ant and the rope to measure this apparent weight.] The magnitude of the maximum acceleration of the SHM is mω. But ω = v k = (F / μ) (π / λ). Thus we must require ma(g / μ) (π / λ) = mg, giving A = (μ g / F) (λ / π). Let us check the unit. The unit of μ g is N/m. The unit of (μ g / F) is therefore just /m. The unit of (λ / π) is just m. So their product has the unit of m, which is the right unit for A.
5 (.6) More general sinusoidal wave: (x, t) = A cos (k x ω t + φ ). (a) At t = 0. (x, t = 0) = A cos (k x + φ ). For φ = 0, (x, 0) = A cos (kx): 0 x For φ = π/, (x, 0) = A cos (kx + π/): That is, even at x = 0, is alread cos (π/). 0 x For φ = π/, (x, 0) = A cos (kx + π/): That is, even at x = 0, is alread cos (π/). From this figure, we can see that it is the same as: (x, 0) = A sin (kx). The wave is then given b: (x, 0) = A sin (kx ωt). For φ = π/ = π/ + π/, (x, 0) = A cos (kx +π/): That is, even at x = 0, is alread cos (π/). 0 0 x x For φ = π/ = π + π/, (x, 0) = A cos (kx + π/): That is, even at x = 0, is alread cos (π/). From this figure, we can see that it is the same as: (x, 0) = + A sin (kx). The wave is then given b: (x, 0) = + A sin (kx ωt). 0 x
6 (b) Transverse velocit: v = / t = + Aω sin (k x ω t + φ ). (c) At t = 0, a particle at x = 0 has displacement = A /. Can one determine φ? No. There are several candidates: At t = x = 0, (0, 0) = + A cos (φ ). So we need to demand cos (φ ) = /. The answer is φ = π/ or 7π/. (Note: φ = 7π/ is the same as φ = π/, since their difference is π.) If we also know that a particle at x = 0 is moving toward = 0 at t = 0, determine φ. For x = 0, (0, t) = A cos ( ω t + φ ). We test φ = π/ and 7π/, and see which one works. We first calculate the transverse velocit v = / t = + Aω sin ( ω t + φ ), and evaluate it at t = 0, and get v (x = 0, t = 0) = + Aω sin (φ ). At φ = π/, this transverse velocit is positive, so it is not moving toward =0. So we reject it. At φ = 7π/, this transverse velocit is negative, so it is moving toward =0. So we accept this answer. Hence we conclude that φ = 7π/ (or, equivalentl, π/). Can one get this answer without doing so much math? es! First, one should realize that if (x, t) = A cos (kx ωt + φ), then the wave is moving toward positive x, or to the right in our plots. Then looking at our plot for φ = π/, and let the curve move to the right. One will find that will increase. at x = 0. So we should reject this answer. Then we do the same thing for φ = 7π/ or π/, and see that it can be accepted. (d) In general, to determine φ, we need to know: (i) (x = 0, t = 0); and (ii) the sign of v (x = 0, t = 0). (.68) Vibrating string. 0.0 cm long. Tension F =.00 N. Five stroboscopic pictures shown. Strobo rate is 000 flashes per minute. Maximum displacement occurs at flashes and, with no other maxima in between. P.0 cm.0 cm (a) Period: T = min = s (the time for 8 flashes). Frequenc f = / T = 0. Hz. Wavelength = 0.0 cm. All for either of the two the traveling wave on this string that are moving in opposite directions to form this standing wave. (b) The second harmonic (also known as the first overtone). (c) Speed of the traveling waves on this string v = λ / T = 0.0 cm / (0.096 s) = 0.8 cm/s =. m/s. (d) Point P. (i) In position it is moving with a transverse velocit of v = 0. (ii) In position it is moving with a transverse velocit of v = Aω = A(π f ) =
7 .0 cm (π 0. s ) =.0 cm 6.7 s = 96. cm/s =.96 m/s. (e) Mass of this string m = 0.0 m μ = 0.0 m [.00 N / (. m/s) ] = 0.08 kg = 8. g. (.7) String, Both ends held fixed. Vibrates in the third harmonic. Speed 9 m/s. Frequenc 0 Hz. Amplitude at an antinode is 0.00 cm. λ = 9 m/s / 0 Hz = 0.8 m. (a) Find amplitude of oscillation: (i) at x = 0.0 cm from the left end of the string. The general equation for the standing wave is : (x, t) = 0.00 m sin (π x / 0.8 m) sin (π 0 Hz t ) [We let x = 0 be the left end of the string. We should have the factor sin (π x / 0.8 m) because the left end is a node, and sin 0 = 0 Also, the wavelength is 0.8 m, and so at x = 0.8 m we should get sin (π) = 0.] So the amplitude of transverse oscillation at x = 0.0 cm is: 0.00 m sin (π 0 cm / 0.8 m) = 0. (ii) at x = 0.0 cm from the left end of the string, the amplitude is: 0.00 cm sin (π 0 cm / 0.8 m) = 0.00 cm. (iii) at x = 0.0 cm from the left end of the string, the amplitude is: 0.00 cm sin (π 0 cm / 0.8 m) = 0.8 cm/s. (b) At each point of part (a), find time to go from largest upward displacement to largest downward displacement. The answer is the same, and is equal to: T /, or / ( f ) = s, except at the nodes of the standing wave, i.e., at x = 0.0 cm in the three cases of part (a). (c) Maximum transverse velocit of the motion: v (x, t) = (x, t) / t = 0.00 cm (π 0 Hz) sin (π x / 0.8 m) cos (π 0 Hz t ) The amplitude of transverse velocit at distance x from the left end is 0.00 m (π 0 Hz) sin (π x / 0.8 m). So at x = 0.0 cm from the left end of the string, the maximum transverse velocit is: 0.00 m (π 0 Hz) sin (π 0.0 m / 0.8 m) = 0. at x = 0.0 cm from the left end of the string, the maximum transverse velocit is: 0.00 cm (π 0 Hz) sin (π 0.0 m / 0.8 m) = 60. cm/s = 6.0 m/s. at x = 0.0 cm from the left end of the string, the maximum transverse velocit is: 0.00 cm (π 0 Hz) sin (π 0.0 m / 0.8 m) = 6. cm/s =.7 m/s. Maximum transverse acceleration of the motion: a (x, t) = v (x, t) / t = 0.00 cm (π 0 Hz) sin (π x / 0.8 m) sin (π 0 Hz t ) The amplitude of transverse acceleration at distance x from the left end is 0.00 m (π 0 Hz) sin (π x / 0.8 m). So at x = 0.0 cm from the left end of the string, the maximum transverse acceleration is: 0.00 m (π 0 Hz) sin (π 0.0 m / 0.8 m) = 0. at x = 0.0 cm from the left end of the string, the maximum transverse acceleration is: 0.00 cm (π 0 Hz) sin (π 0.0 m / 0.8 m) =
8 60. cm/s = cm/s = 9096 m/s. at x = 0.0 cm from the left end of the string, the maximum transverse accelration is: 0.00 cm (π 0 Hz) sin (π 0.0 m / 0.8 m) = 67 cm/s = 6 m/s. Actuall, these answers are eas to see b looking at the figure: The second node from the left end is at 0.8 m, because ou see a whole wavelength between here and the left end. Then the first node from the left end must be at 0. m. The first antinode from the left end must be at 0. m. This is wh at x = 0. m we find the largest amplitudes of velocit and acceleration, and at x = 0. m we find vanishing amplitudes of velocit and acceleration. In addition, the amplitudes of velocit and acceleration at x = 0. m is down from those at x = 0. m b a factor sin (π/) = / = 0.707, as the xdependent factor is simpl a sine function to give sin (π/) = at x = 0. m, and to give sin (π) = 0 at x = 0. m. It will also give 0 at x = 0.8 m, and at x =. m, which is the right end of the string. The correspond to sin (π) and sin (π) from the xdependent factor.
Chapter 18 4/14/11. Superposition Principle. Superposition and Interference. Superposition Example. Superposition and Standing Waves
Superposition Principle Chapter 18 Superposition and Standing Waves If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum
More informationSOLUTIONS TO CONCEPTS CHAPTER 15
SOLUTIONS TO CONCEPTS CHAPTER 15 1. v = 40 cm/sec As velocity of a wave is constant location of maximum after 5 sec = 40 5 = 00 cm along negative xaxis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L
More informationSuperposition and Standing Waves. Solutions of Selected Problems
Chapter 18 Superposition and Standing Waves. s of Selected Problems 18.1 Problem 18.8 (In the text book) Two loudspeakers are placed on a wall 2.00 m apart. A listener stands 3.00 m from the wall directly
More informationUnit 6 Practice Test: Sound
Unit 6 Practice Test: Sound Name: Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. A mass attached to a spring vibrates back and forth. At
More informationSimple Harmonic Motion Concepts
Simple Harmonic Motion Concepts INTRODUCTION Have you ever wondered why a grandfather clock keeps accurate time? The motion of the pendulum is a particular kind of repetitive or periodic motion called
More informationWaves I: Generalities, Superposition & Standing Waves
Chapter 5 Waves I: Generalities, Superposition & Standing Waves 5.1 The Important Stuff 5.1.1 Wave Motion Wave motion occurs when the mass elements of a medium such as a taut string or the surface of a
More informationSolution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k
Physics 1C Midterm 1 Summer Session II, 2011 Solutions 1. If F = kx, then k m is (a) A (b) ω (c) ω 2 (d) Aω (e) A 2 ω Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of
More informationStandard Expression for a Traveling Wave
Course PHYSICS260 Assignment 3 Due at 11:00pm on Wednesday, February 20, 2008 Standard Expression for a Traveling Wave Description: Identify independant variables and parameters in the standard travelling
More informationChapter4: Superposition and Interference
Chapter4: Superposition and Interference Sections Superposition Principle Superposition of Sinusoidal Waves Interference of Sound Waves Standing Waves Beats: Interference in Time Nonsinusoidal Wave Patterns
More information16.2 Periodic Waves Example:
16.2 Periodic Waves Example: A wave traveling in the positive x direction has a frequency of 25.0 Hz, as in the figure. Find the (a) amplitude, (b) wavelength, (c) period, and (d) speed of the wave. 1
More informationphysics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves
Chapter 20 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide
More informationStanding Waves on a String
1 of 6 Standing Waves on a String Summer 2004 Standing Waves on a String If a string is tied between two fixed supports, pulled tightly and sharply plucked at one end, a pulse will travel from one end
More informationSound Waves. PHYS102 Previous Exam Problems CHAPTER. Sound waves Interference of sound waves Intensity & level Resonance in tubes Doppler effect
PHYS102 Previous Exam Problems CHAPTER 17 Sound Waves Sound waves Interference of sound waves Intensity & level Resonance in tubes Doppler effect If the speed of sound in air is not given in the problem,
More informationMechanical Vibrations
Mechanical Vibrations A mass m is suspended at the end of a spring, its weight stretches the spring by a length L to reach a static state (the equilibrium position of the system). Let u(t) denote the displacement,
More informationPhysics 9 Fall 2009 Homework 2  Solutions
Physics 9 Fall 009 Homework  s 1. Chapter 7  Exercise 5. An electric dipole is formed from ±1.0 nc charges spread.0 mm apart. The dipole is at the origin, oriented along the y axis. What is the electric
More informationChapter 13, example problems: x (cm) 10.0
Chapter 13, example problems: (13.04) Reading Fig. 1330 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapter 20. Traveling Waves You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It
More informationSpring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations
Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring
More information1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.
practice wave test.. Name Use the text to make use of any equations you might need (e.g., to determine the velocity of waves in a given material) MULTIPLE CHOICE. Choose the one alternative that best completes
More information08/19/09 PHYSICS 223 Exam2 NAME Please write down your name also on the back side of this exam
08/19/09 PHYSICS 3 Exam NAME Please write down your name also on the back side of this exam 1. A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s. 1A. How far apart (in units of cm) are two
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME  TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More informationAP Physics C. Oscillations/SHM Review Packet
AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete
More informationPhysics 231 Lecture 15
Physics 31 ecture 15 Main points of today s lecture: Simple harmonic motion Mass and Spring Pendulum Circular motion T 1/f; f 1/ T; ω πf for mass and spring ω x Acos( ωt) v ωasin( ωt) x ax ω Acos( ωt)
More informationSTANDING WAVES. Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave.
STANDING WAVES Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave. Apparatus: Magnetic oscillator, string, mass hanger and assorted masses, pulley,
More informationChapter 11. Waves & Sound
Chapter 11 Waves & Sound 11.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position.
More informationSPH3UW Superposition and Interference Page 1 of 6
SPH3UW Superposition and Interference Page 1 of 6 Notes Physics Tool box Constructive Interference: refers to when waves build up each other, resulting in the medium having larger amplitude. Destructive
More information第 1 頁, 共 8 頁 Chap16&Chap17 1. Test Bank, Question 6 Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are (x,t) = y m sin(3x 6t), y 2
More informationMathematical Physics
Mathematical Physics MP205 Vibrations and Waves Lecturer: Office: Lecture 19 Dr. Jiří Vala Room 1.9, Mathema
More informationThe Physics of Guitar Strings
The Physics of Guitar Strings R. R. McNeil 1. Introduction The guitar makes a wonderful device to demonstrate the physics of waves on a stretched string. This is because almost every student has seen a
More informationMAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START
Laboratory Section: Last Revised on September 21, 2016 Partners Names: Grade: EXPERIMENT 11 Velocity of Waves 0. PreLaboratory Work [2 pts] 1.) What is the longest wavelength at which a sound wave will
More informationPHYS 1014M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 1014M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationS15AP Phys Q3 SHOSound PRACTICE
Name: Class: Date: ID: A S5AP Phys Q3 SHOSound PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question.. If you are on a train, how will the pitch of the
More informationSimple Harmonic Motion
Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights
More informationInterference: Two Spherical Sources
Interference: Two Spherical Sources Superposition Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase Superposition Traveling waves move through
More informationPhysics 1120: Simple Harmonic Motion Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* PHYSICS 9702/02 Paper 2 AS Level Structured Questions For Examination from 2016 SPECIMEN
More informationA B C D. Sensemaking TIPERs Instructors Manual Part E & F Copyright 2015 Pearson Education, Inc. 3
E WAVES ERT0: WAVES WAVELENGTH The drawings represent snapshots taken of waves traveling to the right along strings. The grids shown in the background are identical. The waves all have speed, but their
More information226 Chapter 15: OSCILLATIONS
Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion
More informationLesson 11. Luis Anchordoqui. Physics 168. Tuesday, December 8, 15
Lesson 11 Physics 168 1 Oscillations and Waves 2 Simple harmonic motion If an object vibrates or oscillates back and forth over same path each cycle taking same amount of time motion is called periodic
More informationChapter 15: Making Waves
Chapter 15: Making Waves 1. Electromagnetic waves are generally A. transverse waves. B. longitudinal waves. C. a 50/50 combination of transverse and longitudinal waves. D. standing waves. 2. The period
More informationWaves. Sec Wave Properties. Waves are everywhere in nature. What is a wave? Example: Slinky Wave
Waves PART I Wave Properties Wave Anatomy PART II Wave Math Wave Behavior PART III Sound Waves Light Waves (aka Electromagnetic Waves or Radiation) 1 Sec. 14.1 Wave Properties Objectives Identify how waves
More informationRotational Mechanics  1
Rotational Mechanics  1 The Radian The radian is a unit of angular measure. The radian can be defined as the arc length s along a circle divided by the radius r. s r Comparing degrees and radians 360
More informationSimple Harmonic Motion(SHM) Harmonic Motion and Waves. Period and Frequency. Period and Frequency
Simple Harmonic Motion(SHM) Harmonic Motion and Waves Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period
More informationChapter 21. Superposition
Chapter 21. Superposition The combination of two or more waves is called a superposition of waves. Applications of superposition range from musical instruments to the colors of an oil film to lasers. Chapter
More information= mg [down] =!mg [up]; F! x
Section 4.6: Elastic Potential Energy and Simple Harmonic Motion Mini Investigation: Spring Force, page 193 Answers may vary. Sample answers: A. The relationship between F g and x is linear. B. The slope
More informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More informationHW2 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.
HW2 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 15.P.041 The wave function for a harmonic wave on a string
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationAdvanced Higher Physics: MECHANICS. Simple Harmonic Motion
Advanced Higher Physics: MECHANICS Simple Harmonic Motion At the end of this section, you should be able to: Describe examples of simple harmonic motion (SHM). State that in SHM the unbalanced force is
More informationPhysics 271 FINAL EXAMSOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath
Physics 271 FINAL EXAMSOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationSimple Harmonic Motion
Simple Harmonic Motion 9M Object: Apparatus: To determine the force constant of a spring and then study the harmonic motion of that spring when it is loaded with a mass m. Force sensor, motion sensor,
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationOscillations. Vern Lindberg. June 10, 2010
Oscillations Vern Lindberg June 10, 2010 You have discussed oscillations in Vibs and Waves: we will therefore touch lightly on Chapter 3, mainly trying to refresh your memory and extend the concepts. 1
More informationStanding Waves Physics Lab I
Standing Waves Physics Lab I Objective In this series of experiments, the resonance conditions for standing waves on a string will be tested experimentally. Equipment List PASCO SF9324 Variable Frequency
More informationA Simple Introduction to Interference
Course PHYSICS260 Assignment 4 Due at 11:00pm on Wednesday, February 27, 2008 A Simple Introduction to Interference Description: Interference is discussed for pulses on strings and then for sinusoidal
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationWaves Review Checklist Pulses 5.1.1A Explain the relationship between the period of a pendulum and the factors involved in building one
5.1.1 Oscillating Systems Waves Review Checklist 5.1.2 Pulses 5.1.1A Explain the relationship between the period of a pendulum and the factors involved in building one Four pendulums are built as shown
More informationName Class Date. A wave is produced that moves out from the center in an expanding circle. The wave
Exercises 25.1 Vibration of a Pendulum (page 491) 1. The time it takes for one backandforth motion of a pendulum is called the period. 2. List the two things that determine the period of a pendulum.
More informationLesson 19: Mechanical Waves!!
Lesson 19: Mechanical Waves Mechanical Waves There are two basic ways to transmit or move energy from one place to another. First, one can move an object from one location to another via kinetic energy.
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationResonance. Wave. Wave. There are three types of waves: Tacoma Narrows Bridge Torsional Oscillation. Mechanical Waves 11/2/2009
Resonance Wave Transfers Energy Without Transferring Matter Clip from Mechanical Universe Wave A wave can be described as a disturbance that travels through a medium from one location to another location.
More informationWave topics 1. Waves  multiple choice
Wave topics 1 Waves  multiple choice When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object (a) is at its highest point. (b) is at
More informationGeneral Physics (PHY 2130)
General Physics (PHY 2130) Lecture 28 Waves standing waves Sound definitions standing sound waves and instruments Doppler s effect http://www.physics.wayne.edu/~apetrov/phy2130/ Lightning Review Last lecture:
More information18 Q0 a speed of 45.0 m/s away from a moving car. If the car is 8 Q0 moving towards the ambulance with a speed of 15.0 m/s, what Q0 frequency does a
First Major T042 1 A transverse sinusoidal wave is traveling on a string with a 17 speed of 300 m/s. If the wave has a frequency of 100 Hz, what 9 is the phase difference between two particles on the
More informationAnswer, Key Homework 3 David McIntyre 1
Answer, Key Homewor 3 Daid McIntyre 1 This printout should hae 26 questions, chec that it is complete Multiplechoice questions may continue on the next column or page: find all choices before maing your
More informationPhysics 2101, First Exam, Fall 2007
Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the
More informationPHYS 100 Introductory Physics Sample Exam 2
PHYS 00 Introductory Physics Sample Exam Formulas: Acceleration due to Gravity = 0 m/s Weight = Mass x Acceleration due to Gravity Work = Force x Distance Gravitational Potential Energy = Weight x Height
More informationMatter Waves. Home Work Solutions
Chapter 5 Matter Waves. Home Work s 5.1 Problem 5.10 (In the text book) An electron has a de Broglie wavelength equal to the diameter of the hydrogen atom. What is the kinetic energy of the electron? How
More informationColumbia University Department of Physics QUALIFYING EXAMINATION
Columbia University Department of Physics QUALIFYING EXAMINATION Monday, January 13, 2014 1:00PM to 3:00PM Classical Physics Section 1. Classical Mechanics Two hours are permitted for the completion of
More information11/17/10. Transverse and Longitudinal Waves. Transverse and Longitudinal Waves. Wave Speed. EXAMPLE 20.1 The speed of a wave pulse
You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It s less apparent that sound
More informationCenter of Mass/Momentum
Center of Mass/Momentum 1. 2. An Lshaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the Lshaped
More informationConstructive and Destructive Interference Conceptual Question
Chapter 16  solutions Constructive and Destructive Interference Conceptual Question Description: Conceptual question on whether constructive or destructive interference occurs at various points between
More informationG r a d e 1 1 P h y s i c s ( 3 0 s )
G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice exam answer Key G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice Exam Answer Key Instructions The final exam will be weighted as follows: Modules
More informationCutnell/Johnson Physics
Cutnell/Johnson Physics Classroom Response System Questions Chapter 17 The Principle of Linear Superposition and Interference Phenomena Interactive Lecture Questions 17.1.1. The graph shows two waves at
More informationChapter 1. Oscillations. Oscillations
Oscillations 1. A mass m hanging on a spring with a spring constant k has simple harmonic motion with a period T. If the mass is doubled to 2m, the period of oscillation A) increases by a factor of 2.
More information201. Sections Covered in the Text: Chapter 21, except The Principle of Superposition
Superposition Sections Covered in the Text: Chapter 21, except 21.8 In Note 18 we saw that a wave has the attributes of displacement, amplitude, frequency, wavelength and speed. We can now consider the
More informationObjectives 354 CHAPTER 8 WAVES AND VIBRATION
Objectives Describe how a mechanical wave transfers energy through a medium. Explain the difference between a transverse wave and a longitudinal wave. Define amplitude and wavelength. Define frequency
More informationTest  A2 Physics. Primary focus Magnetic Fields  Secondary focus electric fields (including circular motion and SHM elements)
Test  A2 Physics Primary focus Magnetic Fields  Secondary focus electric fields (including circular motion and SHM elements) Time allocation 40 minutes These questions were ALL taken from the June 2010
More informationSimple Harmonic Motion Experiment. 1 f
Simple Harmonic Motion Experiment In this experiment, a motion sensor is used to measure the position of an oscillating mass as a function of time. The frequency of oscillations will be obtained by measuring
More informationUnit  6 Vibrations of Two Degree of Freedom Systems
Unit  6 Vibrations of Two Degree of Freedom Systems Dr. T. Jagadish. Professor for Post Graduation, Department of Mechanical Engineering, Bangalore Institute of Technology, Bangalore Introduction A two
More information1 of 10 11/23/2009 6:37 PM
hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction
More informationAP Physics B Free Response Solutions
AP Physics B Free Response Solutions. (0 points) A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The anchor is suspended by a rope of negligible
More informationPHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17. February 13, 2013
PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17 February 13, 2013 0.1 A 2.00kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object
More informationPhysics 53. Wave Motion 1
Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can
More informationNotice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.
HW1 Possible Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 14.P.003 An object attached to a spring has simple
More informationHOOKE S LAW AND SIMPLE HARMONIC MOTION
HOOKE S LAW AND SIMPLE HARMONIC MOTION Alexander Sapozhnikov, Brooklyn College CUNY, New York, alexs@brooklyn.cuny.edu Objectives Study Hooke s Law and measure the spring constant. Study Simple Harmonic
More informationturntable in terms of SHM and UCM: be plotted as a sine wave. n Think about spinning a ball on a string or a ball on a
RECALL: Angular Displacement & Angular Velocity Think about spinning a ball on a string or a ball on a turntable in terms of SHM and UCM: If you look at the ball from the side, its motion could be plotted
More informationLABORATORY 9. Simple Harmonic Motion
LABORATORY 9 Simple Harmonic Motion Purpose In this experiment we will investigate two examples of simple harmonic motion: the massspring system and the simple pendulum. For the massspring system we
More informationSOLID MECHANICS DYNAMICS TUTORIAL NATURAL VIBRATIONS ONE DEGREE OF FREEDOM
SOLID MECHANICS DYNAMICS TUTORIAL NATURAL VIBRATIONS ONE DEGREE OF FREEDOM This work covers elements of the syllabus for the Engineering Council Exam D5 Dynamics of Mechanical Systems, C05 Mechanical and
More informationDetermination of g using a spring
INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative
More informationGiant Slinky: Quantitative Exhibit Activity
Name: Giant Slinky: Quantitative Exhibit Activity Materials: Tape Measure, Stopwatch, & Calculator. In this activity, we will explore wave properties using the Giant Slinky. Let s start by describing the
More informationPhysics 18 Spring 2011 Homework 13  Solutions Wednesday April 20, 2011
Physics 18 Spring 011 Homework 13  s Wednesday April 0, 011 Make sure your name is on your homework, and please box your final answer. Because we will be giing partial credit, be sure to attempt all the
More information1/26/2016. Chapter 21 Superposition. Chapter 21 Preview. Chapter 21 Preview
Chapter 21 Superposition Chapter Goal: To understand and use the idea of superposition. Slide 212 Chapter 21 Preview Slide 213 Chapter 21 Preview Slide 214 1 Chapter 21 Preview Slide 215 Chapter 21
More informationType: Double Date: Simple Harmonic Motion III. Homework: Read 10.3, Do CONCEPT QUEST #(7) Do PROBLEMS #(5, 19, 28) Ch. 10
Type: Double Date: Objective: Simple Harmonic Motion II Simple Harmonic Motion III Homework: Read 10.3, Do CONCEPT QUEST #(7) Do PROBLEMS #(5, 19, 28) Ch. 10 AP Physics B Mr. Mirro Simple Harmonic Motion
More informationW i f(x i ) x. i=1. f(x i ) x = i=1
Work Force If an object is moving in a straight line with position function s(t), then the force F on the object at time t is the product of the mass of the object times its acceleration. F = m d2 s dt
More information