Lesson 11. Luis Anchordoqui. Physics 168. Tuesday, December 8, 15

Size: px
Start display at page:

Download "Lesson 11. Luis Anchordoqui. Physics 168. Tuesday, December 8, 15"

Transcription

1 Lesson 11 Physics 168 1

2 Oscillations and Waves 2

3 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 Mass and spring system is useful model for a periodic system 3

4 Simple harmonic motion (cont d) We assume that surface is frictionless There is a point where spring is neither stretched nor compressed Equilibrium position We measure displacement from that point (x = 0) Force exerted by spring depends on displacement F = kx 4

5 Simple harmonic motion (cont d) Minus sign on force indicates that it is a restoring force it is directed to restore mass to its equilibrium position k is spring constant Force is not constant so acceleration is not constant either 5

6 Simple harmonic motion (cont d) Displacement is measured from equilibrium point Amplitude is maximum displacement A cycle is a full to-and-from motion Period is time required to complete one cycle Frequency is number of cycles completed per second 6

7 Simple harmonic motion (cont d) Any vibrating system where restoring force is proportional to negative of displacement is in simple harmonic motion (SHM) and is often called a simple harmonic oscillator We know that potential energy of a spring is given by PE = 1 2 kx2 Total mechanical energy is then: E = 1 2 mv kx2 Total mechanical energy will be conserved as we are assuming system is frictionless 7

8 Energy in simple harmonic oscillator If mass is at limits of its motion energy is all potential If mass is at equilibrium point energy is all kinetic We know what potential energy is at turning points 8

9 Period and sinusoidal nature of SHM Figure shows how to get experimentally versus t for a mass on a spring A marking pen is attached to a mass on a spring and paper is pulled to left As paper moves with constant speed pen traces out displacement x x as a function of time General equation for such curve is x = A cos (!t + ) 2 f Phase constant 9

10 Sinusoidal Nature of SHM Consider an object on a spring on a frictionless surface Equilibrium F x = kx Using Newton s second law m d2 x dt 2 = kx General solution is x = A cos (!t + ) 10

11 Sinusoidal Nature of SHM (cont d) Velocity and acceleration can be calculated as function of time Displacement x v = v max sin!t v max = A (k/m) 1 2 Velocity v a = a max cos (2 t/t ) a max = k A/m Acceleration a 11

12 Spider Web A spider of mass 0.3 g waits in its web of negligible mass A slight movement causes the web to vibrate with a frequency of about 15 Hz a) Estimate value of spring stifness constant k for web (b) At what frequency would you expect web to vibrate if an insect of mass 0.1 g were trapped in addition to spider? 12

13 Frequency of SHM is given by = 1 r k 2 m ) k =(2 )2 m =2.7 N/m For m = kg we have = 1 r k 2 m = 13 Hz 13

14 Oscillating systems: object on a vertical spring X Fy = ky + mg Changing variables y 0 = y y 0 X Fy = k(y 0 + y 0 )+mg But ky 0 = mg! X F y = ky 0 From Newton s second law ky 0 = m d2 y dt 2 dy = dy 0 Solution is y 0 = A cos (!t + )! =(k/m) 1 2 d 2 y 0 dt 2 = k m y0 14

15 For small Oscillating systems: simple pendulum where arc length Repeatedly differentiating on both sides of d 2 s dt 2 Substituting and re-arranging gives gives Note that motion of pendulum does not depend on its mass! sin d 2 mg sin dt 2 g L d 2 General solution for small oscillation = m d2 s dt 2 s = L = L d2 dt 2 dt 2 = g L sin s 1 = 0 cos(!t + ) Where! 2 = g L and T = 2! =2 (L/g)

16 sin at small angles (Degrees) (Radians) sin % Difference % % 0.5% 1.1% 2.0% % 16

17 Energy in a simple harmonic motion U = 1 2 kx2 U = 1 2 ka2 cos 2 (!t + ) K = 1 2 mv2 K = 1 2 m!2 A 2 sin 2 (!t + ) Using! 2 = k/m E = U + K = 1 2 ka2 [cos 2 (!t + )+sin 2 (!t + )] = 1 2 ka2 17

18 Wave Motion A mechanical wave is caused by a disturbance in a medium As wind passes over water's surface friction forces it to ripple Strength of wind, distance wind blows, and duration determine how big ripples will become Crest is highest point on wave Trough is lowest point on wave Wavelength is horizontal distance either between crests or troughs of two consecutive waves Wave height is vertical distance between wave's crest and next trough Wave period measures size of wave in time 18

19 Wave Motion (cont d) If you have ever watched ocean waves moving toward shore before they break you may have wondered if waves were carrying water from far out at sea into beach Water moves with a recognizable velocity but each molecule of water itself This is clearly demonstrated by observing a bottle on a pond as waves move by Bottle is not carried forward by waves, but simply oscillate about an Water droplet move in a vertical circle as wave passes Droplet moves forward with wave's crest and backward with trough These vertical circles are more obvious at surface merely oscillates about an equilibrium point equilibrium point because this is motion of water itself As depth increases their effects slowly decrease until completely disappearing about half a wavelength below surface 19

20 Looking a little more closely at how a wave its form and how it comes to travel: A single wave bump or pulse can be formed on a rope by a quick up-and-down motion of hand Figure shows a pulse on a string at time Shape of string at this instant can be represented by some function String is described in this frame by At some later time pulse is farther down string for all times x-coordinates of two reference frames are related by Shape of string in original reference frame is f(x 0 )=f(x Pulse In a new coordinate system with origin that moves to right with same speed as pulse f(x 0 ) Same line of reasoning for a pulse moving to left leads to pulse is stationary x 0 = x wave moving in t =0 y = f(x) direction 20 vt) +x vt O 0 y = f(x + vt)

21 Looking a little more closely at how a wave its form and how it comes to travel: Periodic wave A continuous or periodic wave has as its source a disturbance that is continuous and oscillating disturbance in this case is change in shape of string Its propagation arises from interaction of each string segment with adjacent segments Segments of string move in direction perpendicular to string as pulses that propagate back and forth along string 21

22 Types of waves Waves in which motion of medium (molecules of water, particles on string) is perpendicular to direction of propagation are called transverse waves Waves in which motion of medium is along (parallel to) direction of propagation of disturbance are called longitudinal waves (Sound waves are examples of longitudinal waves) 22

23 Speed of waves Speed of waves relative to medium depends on elastic and inertial properties of medium but is independent of motion of source of waves String tension For a pulse on a rope v = FT µ 1 2 Linear mass density Bulk modulus For sounds waves v = B 1 2 Volume mass density 23

24 Graphic representations of a sound wave (A) Air at equilibrium in absence of a sound wave (B) Compressions and rarefactions that constitute a sound wave (C) Transverse representation of wave showing amplitude (A) and wavelength (λ) 24

25 Speed of sound in air For sound waves in a gas bulk modulus is proportional to pressure which in turn is proportional to density and to absolute temperature of gas Ratio B/ is independent of density and is merely proportional to absolute temperature Dimensionless constant For diatomic molecules such as O 2 depends on kind of gas Because and comprise of atmosphere for air For gases composed of monoatomic molecules such as Molar mass from air is Speed of sound at v =( RT/M) O 2 N 2 N 2 98% =7/5= 7/5 H e =5/3 T [K] = T [ C] R = J/(mol K) M = kg/mol 20 C is about 343 m/s and

26 Explosion of a depth charge beneath surface of a body of water is recorded by an helicopter hovering above water's surface as shown in figure Along which path (A, B, or, C) will sound wave take least time to reach helicopter? 26

27 Explosion of a depth charge beneath surface of a body of water is recorded by an helicopter hovering above water's surface as shown in figure Along which path (A, B, or, C) will sound wave take least time to reach helicopter? Speed of sound in water is greater than speed of sound in air path C fluis are almost incompressible implies disturbance propagates very quickly 27

28 Wave intensity Wave transports energy from one place to another As waves travel through a medium energy is transferred as vibrational energy from a particle to particle in medium If a point source emits waves uniformly in all directions then energy at a distance r from source is distributed uniformly on a spherical surface of radius r and area A =4 r 2 Average power per unit area that is incident perpendicular to direction of propagation is called intensity I = hp i A 28

29 Doppler Effect You may have noticed that you hear higher pitch of whistle on a speeding train dropped abruptly as it passes you This phenomenon is known as Doppler effect 29

30 Doppler Effect (cont d) Consider whistle of a train at rest which is emitting sound of a particular frequency in all directions as shown in figure Sound waves are moving at speed of sound in air which is independent of velocity of source or observer If our source is moving then whistle emits sounds at same frequency as it does at rest Sound wavefronts it emits forward are closer together than when train is at rest This is because train as it moves is chasing previously emitted wavefronts and emits each crest closer to previous one Thus an observer in front of train will detect more wave crests passing per second so frequency heard is higher Wavefronts emitted behind train are farther apart than when train is at rest because train is speeding away from them Fewer wave crest per second pass by an observer behind moving train and perceived pitch is lower 30

31 Doppler Effect (cont d) In following discussion all motions are relative to medium Consider a source moving with speed u s and a stationary receiver Source has frequency Received frequency (number of crests passing receiver per unit time) is related to wavelength (distance between successive crests) and wave speed v by f s f r = v 31

32 Time between these two events is Doppler Effect (cont d) t 1 and next wave crest leaves source at time t 2 T s = t 2 t 1 A wave crest leaves source at time and during this time source and crest leaving source at time t 1 u s T s vt s travel distances and respectively At time t 2 distance between source and crest leaving at time t 1 equals wavelength 32

33 Doppler Effect (cont d) If u s <v Behind source We can express both = b =(v + u s ) T s In front of source Substituting for our expression for f r = v = = f =(v u s ) T s b 33 and v v ± u s f s f as =(v ± u s )T s = v ± u s f s and rearranging (stationary receiver)

34 Doppler Effect (cont d) When receiver moves with respect to medium received frequency is different because receiver moves past more or fewer wave crests in a given time Let T r denote time between arrivals of successive crests for a receiver moving with speed u r During time between arrivals of two successive crests each crest will have traveled a distance vt r and during same time receiver will have traveled a distance u r T r If receiver moves in direction opposite to wave during a time distance a wave moves + distance receiver moves equals wavelength vt r + u r T r =! T r = /(v + u r ) If receiver moves in same direction as wave vt r u r T r =! T r = /(v u r ) 34 T

35 Doppler Effect (cont d) Because f r = /T Substituting for we have f = 1 T r = v ± u r r f r = v ± u r v ± u s f s In a reference frame in which medium is moving (e.g. reference frame of ground if air is medium and there is a wind blowing) Wave speed v is replaced by v 0 = v ± u w where u w is velocity of wind relative to ground 35

36 Batman has sent a signal to batcave calling for his batfriends to cover his escape Answering signal, a bat which is nearby starts flying at 5 m/s As it flies, bat emits an ultrasonic sound wave with frequency 30 khz towards tall wall of building What frequency does bat hear in reflected wave? 36

37 The wall is treated as stationary observer for calculation frequency it receives Bat is flying towards wall so f 0 wall = f bat 1 1 v bat /v sound Wall is treated as stationary source emitting frequency f 0 wall and bat as moving observer flying towards wall f 00 bat = f 0 wall 1+ v bat v sound = f bat 1 1 v bat /v sound v sound + v bat = f bat = Hz v sound v bat 1+ v bat v sound 37

38 Shock Waves During our derivations of Doppler-shift expressions we assumed that speed u of source was less than wave speed v If source moves with speed greater than wave speed there will be no waves in from of source Instead waves pile-up behind source to form a shock wave In case of sound waves this shock wave is heard as a sonic boom when it arrives at receiver 38

39 Shock waves produced by a bullet traversing a helium balloon 39

40 Mach Number P 1 P 1 Figure shows a source originally at point After some time t wave emitted from point Source has traveled a distance moving to right with velocity u has traveled a distance ut and will be at point Line from this new position of source to wavefront emitted when source was at P 1 vt P 2 makes an angle with path of source known as Mach angle + sin = vt ut = v u Shock wave is confined to a cone that narrows as u v u increases Ratio of source speed to wave speed is called Mach number Mach number = u v 40

41 Sonic Boom Shock waves from a supersonic plane Luis Anchordoqui 41

42 A supersonic plane flying due east at an altitude of 15 km passes directly over point P Sonic boom is heard at point P when plane is 22 km east of point P What is speed of plane? 42

43 A supersonic plane flying due east at an altitude of 15 km passes directly over point P Sonic boom is heard at point P when plane is 22 km east of point P What is speed of plane? Velocity = 610 m/s 43

44 Doppler Effect (summary) Stationary Sound Source Doppler Shift Source moving with v source <v sound Breaking Sound Barrier Sonic Boom Source moving with v source >v sound 44

1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.

1) 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 information

physics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves

physics 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 information

AP Physics C. Oscillations/SHM Review Packet

AP 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 information

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 information

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines Simple Harmonic Motion(SHM) Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period (T) Time for one complete

More information

Physics 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 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 information

Physical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect

Physical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect Objectives: PS-7.1 Physical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect Illustrate ways that the energy of waves is transferred by interaction with

More information

Physics 41 HW Set 1 Chapter 15

Physics 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 information

Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k

Solution: 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 information

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

www.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 information

Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations

Spring 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 information

State Newton's second law of motion for a particle, defining carefully each term used.

State Newton's second law of motion for a particle, defining carefully each term used. 5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

More information

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to :

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to : PROGRESSIVE WAVES 1 Candidates should be able to : Describe and distinguish between progressive longitudinal and transverse waves. With the exception of electromagnetic waves, which do not need a material

More information

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

More information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Ch 25 Chapter Review Q & A s

Ch 25 Chapter Review Q & A s Ch 25 Chapter Review Q & A s a. a wiggle in time is called? b. a wiggle in space & time is called? a. vibration b. wave What is the period of a pendulum? The period is the time for 1 cycle (back & forth)

More information

Exam 4 Review Questions PHY 2425 - Exam 4

Exam 4 Review Questions PHY 2425 - Exam 4 Exam 4 Review Questions PHY 2425 - Exam 4 Section: 12 2 Topic: The Center of Gravity Type: Conceptual 8. After a shell explodes at the top of its trajectory, the center of gravity of the fragments has

More information

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level

Cambridge 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 information

16.2 Periodic Waves Example:

16.2 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 information

Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

More information

Exercises on Oscillations and Waves

Exercises on Oscillations and Waves Exercises on Oscillations and Waves Exercise 1.1 You find a spring in the laboratory. When you hang 100 grams at the end of the spring it stretches 10 cm. You pull the 100 gram mass 6 cm from its equilibrium

More information

Waves Sound and Light

Waves Sound and Light Waves Sound and Light r2 c:\files\courses\1710\spr12\wavetrans.doc Ron Robertson The Nature of Waves Waves are a type of energy transmission that results from a periodic disturbance (vibration). They are

More information

Chapter 15, example problems:

Chapter 15, example problems: Chapter, example problems: (.0) Ultrasound imaging. (Frequenc > 0,000 Hz) v = 00 m/s. λ 00 m/s /.0 mm =.0 0 6 Hz. (Smaller wave length implies larger frequenc, since their product,

More information

Practice Test SHM with Answers

Practice 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 information

4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet

4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet 4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet Required: READ Hamper pp 115-134 SL/HL Supplemental: Cutnell and Johnson, pp 473-477, 507-513 Tsokos, pp 216-242 REMEMBER TO. Work through all

More information

18 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

18 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 T-042 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 information

Physics 1120: Simple Harmonic Motion Solutions

Physics 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 information

Waves - Transverse and Longitudinal Waves

Waves - Transverse and Longitudinal Waves Waves - Transverse and Longitudinal Waves wave may be defined as a periodic disturbance in a medium that carries energy from one point to another. ll waves require a source and a medium of propagation.

More information

Waves and Sound. AP Physics B

Waves and Sound. AP Physics B Waves and Sound AP Physics B What is a wave A WAVE is a vibration or disturbance in space. A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move. Two types of

More information

UNIT 1: mechanical waves / sound

UNIT 1: mechanical waves / sound 1. waves/intro 2. wave on a string 3. sound waves UNIT 1: mechanical waves / sound Chapter 16 in Cutnell, Johnson: Physics, 8th Edition Properties of waves, example of waves (sound. Light, seismic), Reflection,

More information

SOLUTIONS TO CONCEPTS CHAPTER 15

SOLUTIONS 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 x-axis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L

More information

Periodic wave in spatial domain - length scale is wavelength Given symbol l y

Periodic wave in spatial domain - length scale is wavelength Given symbol l y 1.4 Periodic Waves Often have situations where wave repeats at regular intervals Electromagnetic wave in optical fibre Sound from a guitar string. These regularly repeating waves are known as periodic

More information

Waves-Wave Characteristics

Waves-Wave Characteristics 1. What is the wavelength of a 256-hertz sound wave in air at STP? 1. 1.17 10 6 m 2. 1.29 m 3. 0.773 m 4. 8.53 10-7 m 2. The graph below represents the relationship between wavelength and frequency of

More information

Chapter 21 Study Questions Name: Class:

Chapter 21 Study Questions Name: Class: Chapter 21 Study Questions Name: Class: Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. If a fire engine is traveling toward you, the Doppler

More information

State Newton's second law of motion for a particle, defining carefully each term used.

State Newton's second law of motion for a particle, defining carefully each term used. 5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

More information

Acoustics: the study of sound waves

Acoustics: the study of sound waves Acoustics: the study of sound waves Sound is the phenomenon we experience when our ears are excited by vibrations in the gas that surrounds us. As an object vibrates, it sets the surrounding air in motion,

More information

AS COMPETITION PAPER 2008

AS COMPETITION PAPER 2008 AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. PHYS 101-4M, 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 information

Chapter 8: Potential Energy and Conservation of Energy. Work and kinetic energy are energies of motion.

Chapter 8: Potential Energy and Conservation of Energy. Work and kinetic energy are energies of motion. Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. Consider a vertical spring oscillating with mass m attached to one end. At the extreme ends of travel

More information

HOOKE S LAW AND SIMPLE HARMONIC MOTION

HOOKE 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 information

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013 PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be

More information

VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

More information

Tennessee State University

Tennessee 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 F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

More information

v = λ f this is the Golden Rule for waves transverse & longitudinal waves Harmonic waves The golden rule for waves Example: wave on a string Review

v = λ f this is the Golden Rule for waves transverse & longitudinal waves Harmonic waves The golden rule for waves Example: wave on a string Review L 23 Vibrations and Waves [3] resonance clocks pendulum springs harmonic motion mechanical waves sound waves golden rule for waves musical instruments The Doppler effect Doppler radar radar guns Review

More information

AP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity.

AP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity. 1. A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the

More information

226 Chapter 15: OSCILLATIONS

226 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 information

Solution Derivations for Capa #13

Solution Derivations for Capa #13 Solution Derivations for Capa #13 1 Identify the following waves as T-Transverse, or L-Longitudinal. If the first is T and the rets L, enter TLLL. QUESTION: A The WAVE made by fans at sports events. B

More information

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true? 1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always

More information

PHY121 #8 Midterm I 3.06.2013

PHY121 #8 Midterm I 3.06.2013 PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

More information

Physics 231 Lecture 15

Physics 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 information

Problem Set #8 Solutions

Problem Set #8 Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection

More information

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids 1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

More information

Lecture L22-2D Rigid Body Dynamics: Work and Energy

Lecture L22-2D Rigid Body Dynamics: Work and Energy J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for

More information

Determination of Acceleration due to Gravity

Determination 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 information

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the

More information

Doppler Effect Plug-in in Music Production and Engineering

Doppler Effect Plug-in in Music Production and Engineering , pp.287-292 http://dx.doi.org/10.14257/ijmue.2014.9.8.26 Doppler Effect Plug-in in Music Production and Engineering Yoemun Yun Department of Applied Music, Chungwoon University San 29, Namjang-ri, Hongseong,

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s.

More information

Oscillations. Vern Lindberg. June 10, 2010

Oscillations. 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 information

AP Physics - Chapter 8 Practice Test

AP Physics - Chapter 8 Practice Test AP Physics - Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on

More information

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE 1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object

More information

Chapter 9. particle is increased.

Chapter 9. particle is increased. Chapter 9 9. Figure 9-36 shows a three particle system. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three particle system. (c) What happens to the center of mass

More information

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26 Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,

More information

Simple Harmonic Motion

Simple 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 information

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Wednesday, June 17, 2015 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Wednesday, June 17, 2015 1:15 to 4:15 p.m. P.S./PHYSICS The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS Wednesday, June 17, 2015 1:15 to 4:15 p.m., only The possession or use of any communications

More information

Newton s Law of Motion

Newton s Law of Motion chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating

More information

Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4. Forces and Newton s Laws of Motion. continued Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

More information

C 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

C 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 information

Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

More information

PHY231 Section 1, Form B March 22, 2012

PHY231 Section 1, Form B March 22, 2012 1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate

More information

Columbia University Department of Physics QUALIFYING EXAMINATION

Columbia 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 information

PLEASE DO NOT WRITE ON THE TEST. PLACE ALL MULTIPLE CHOICE ANSWERS ON THE SCANTRON. (THANK YOU FOR SAVING A TREE.)

PLEASE DO NOT WRITE ON THE TEST. PLACE ALL MULTIPLE CHOICE ANSWERS ON THE SCANTRON. (THANK YOU FOR SAVING A TREE.) PLEASE DO NOT WRITE ON THE TEST. PLACE ALL MULTIPLE CHOICE ANSWERS ON THE SCANTRON. (THANK YOU FOR SAVING A TREE.) Sound Waves Test -- each multiple choice question is worth 3 points. 1. Sound waves are

More information

A) F = k x B) F = k C) F = x k D) F = x + k E) None of these.

A) F = k x B) F = k C) F = x k D) F = x + k E) None of these. CT16-1 Which of the following is necessary to make an object oscillate? i. a stable equilibrium ii. little or no friction iii. a disturbance A: i only B: ii only C: iii only D: i and iii E: All three Answer:

More information

9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J

9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J 1. If the kinetic energy of an object is 16 joules when its speed is 4.0 meters per second, then the mass of the objects is (1) 0.5 kg (3) 8.0 kg (2) 2.0 kg (4) 19.6 kg Base your answers to questions 9

More information

Physics 101 Hour Exam 3 December 1, 2014

Physics 101 Hour Exam 3 December 1, 2014 Physics 101 Hour Exam 3 December 1, 2014 Last Name: First Name ID Discussion Section: Discussion TA Name: Instructions Turn off your cell phone and put it away. Calculators cannot be shared. Please keep

More information

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces. Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

More information

Review of Chapter 25. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

Review of Chapter 25. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Review of Chapter 25 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The time needed for a wave to make one complete cycle is its b. velocity.

More information

THE KINETIC THEORY OF GASES

THE KINETIC THEORY OF GASES Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Friday, June 20, 2014 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Friday, June 20, 2014 1:15 to 4:15 p.m. P.S./PHYSICS The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS Friday, June 20, 2014 1:15 to 4:15 p.m., only The possession or use of any communications device

More information

Standing Waves on a String

Standing 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 information

ANALYTICAL METHODS FOR ENGINEERS

ANALYTICAL 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 information

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L - Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates

More information

Unit - 6 Vibrations of Two Degree of Freedom Systems

Unit - 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 information

explain your reasoning

explain your reasoning I. A mechanical device shakes a ball-spring system vertically at its natural frequency. The ball is attached to a string, sending a harmonic wave in the positive x-direction. +x a) The ball, of mass M,

More information

10.1 Quantitative. Answer: A Var: 50+

10.1 Quantitative. Answer: A Var: 50+ Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass

More information

Chapter 7: Momentum and Impulse

Chapter 7: Momentum and Impulse Chapter 7: Momentum and Impulse 1. When a baseball bat hits the ball, the impulse delivered to the ball is increased by A. follow through on the swing. B. rapidly stopping the bat after impact. C. letting

More information

Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

More information

Copyright 2011 Casa Software Ltd. www.casaxps.com

Copyright 2011 Casa Software Ltd. www.casaxps.com Table of Contents Variable Forces and Differential Equations... 2 Differential Equations... 3 Second Order Linear Differential Equations with Constant Coefficients... 6 Reduction of Differential Equations

More information

Work, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions

Work, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.

More information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014 Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

More information

WORK DONE BY A CONSTANT FORCE

WORK DONE BY A CONSTANT FORCE WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newton-meter (Nm) = Joule, J If you exert a force of

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Thursday, June 13, 2013 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS. Thursday, June 13, 2013 1:15 to 4:15 p.m. P.S./PHYSICS The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING PHYSICS Thursday, June 13, 2013 1:15 to 4:15 p.m., only The possession or use of any communications

More information

(Most of the material presented in this chapter is taken from Thornton and Marion, Chap. 7)

(Most of the material presented in this chapter is taken from Thornton and Marion, Chap. 7) Chapter 4. Lagrangian Dynamics (Most of the material presented in this chapter is taken from Thornton and Marion, Chap. 7 4.1 Important Notes on Notation In this chapter, unless otherwise stated, the following

More information

M.Sc Physics Admission Test

M.Sc Physics Admission Test C: EGISTATION NUMBE: M.Sc Physics Admission Test Department of Physics Quaid-i-Aam University Islamabad. September 007 Time: 60 minutes Answer all 0 questions or as many as you can. Each question carries

More information

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N) Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in

More information

Objective: Work Done by a Variable Force Work Done by a Spring. Homework: Assignment (1-25) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout)

Objective: Work Done by a Variable Force Work Done by a Spring. Homework: Assignment (1-25) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout) Double Date: Objective: Work Done by a Variable Force Work Done by a Spring Homework: Assignment (1-25) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout) AP Physics B Mr. Mirro Work Done by a Variable

More information

PHYA2. General Certificate of Education Advanced Subsidiary Examination June 2010. Mechanics, Materials and Waves

PHYA2. General Certificate of Education Advanced Subsidiary Examination June 2010. Mechanics, Materials and Waves Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 2 For this paper you must have: a ruler a calculator a Data and Formulae Booklet.

More information