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38 Pages

### 037- Waves and Sound

Course: PHYSICS 20339841, Spring 2012
School: Aarhus Universitet,...
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Word Count: 1387

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and Waves Sound AP Physics B Aim: What are wave properties? Objectives a) Sketch wave graphs and determine the amplitude, wavelength, and frequency b) Relate wavelength, frequency, and velocity for a wave. c) Explain the Doppler effect for sound. d) Describe reflection of a wave from the fixed or free end of a string. e) Describe qualitatively what factors determine the speed of waves on a string and the speed...

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and Waves Sound AP Physics B Aim: What are wave properties? Objectives a) Sketch wave graphs and determine the amplitude, wavelength, and frequency b) Relate wavelength, frequency, and velocity for a wave. c) Explain the Doppler effect for sound. d) Describe reflection of a wave from the fixed or free end of a string. e) Describe qualitatively what factors determine the speed of waves on a string and the speed of sound. 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 Waves The first type of wave is called Longitudinal. Longitudinal Wave - A fixed point will move parallel with the wave motion 2 areas Compression- an area of high molecular density and pressure Rarefaction - an area of low molecular density and pressure Two types of Waves The second type of wave is called Transverse. Transverse Wave - A fixed point will move perpendicular with the wave motion. Wave parts-crest, trough, wavelength, amplitude, frequency, period Cyclical Motion Period ()= the time for one wave cycle to be completed =1/f Unit: Seconds Frequency (f )=the number of cycles per unit time f=cycles/time OR Unit: Hertz (Hz) f=1/ 1Hz=1cylce/1second Frequency: Sound Waves: PITCH, NOTE high frequency high note Light Waves: COLOR high frequency more "blue" ROYGBIV Wave Speed You can find the speed of a wave by multiplying the wave's wavelength in meters by the frequency (cycles per second). Since a "cycle" is not a standard unit this gives you meters/second. Example A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength? cycles 40 f = = = 1.33 Hz sec 30 x 4.25 v= = = 0.425 m/s t 10 vwave vwave = f = = 0.319 m f Sound Waves Sound Waves are a common type of standing wave as they are caused by RESONANCE. Resonance when a FORCED vibration matches an object's natural frequency thus producing vibration, sound, or even damage. One example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible. http://www.5min.com/Video/The-Original-Tacoma-Narrows-Bridge-Collapse-of-1940-119995718 RESONANCE An oscillating system is in resonance with some driving force whenever the frequency of the driving force matches one of the natural frequencies of the system; the system responds with a large A. Doppler Effect Doppler Effect Doppler effect occurs for all types of waves, water, sound and even light. This is how we know the universe is expanding. SITUATION 3 Moving Source; Stationary Observers As the source moves a distance vS (T=1/f period of wave) toward O1 there is a decrease in the wavelength of sound by a quantity of vs . The shortened wavelength ' becomes ' = vsT The frequency f' of sound wave heard by O1 increases as given by, (6) Moving Source and Observer Wave Barriers The object is moving at the speed of waves in the medium. Shock Waves The source is moving faster than the wave speed in the medium. A shock wave is formed and it is very difficult to break through the previous wave barrier. These waves produce sonic booms. 19 Doppler Example Intelligence tells you that a particular piece of machinery in the engine room of a Victor III submarine emits a frequency of 320 Hz. Your sonar operator hears the machinery but reports the frequency is 325 Hz. Assume you have slowed to a negligible speed in order to better hear the submarine. Is the VIII coming toward you or moving away from you? Assuming the Victor is either moving directly toward or away from you, what is his speed in m/s? Aim: What are standing waves? Objectives Describe a) reflection of a wave from the fixed or free end of a string. b) Describe qualitatively what factors determine the speed of waves on a string and the speed of sound. Standing Waves A standing wave is produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave: Antinodes Areas of MAXIMUM AMPLITUDE Nodes Areas of ZERO AMPLITUDE. Standing Waves Occurs when a wave reflects upon itself and interference causes the pattern Nodes remain stationary Anti nodes-occur half way between nodes Sound Waves The production of sound involves setting up a wave in air. To set up a CONTINUOUS sound you will need to set a standing wave pattern. Three LARGE CLASSES of instruments Stringed - standing wave is set up in a tightly stretched string Percussion - standing wave is produced by the vibration of solid objects Wind - standing wave is set up in a column of air that is either OPEN or CLOSED Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE FIXED ENDS fundamental/1st harmonic 2nd harmonic 3rd harmonic 4th harmonic Normal modes 2L n = n n = 1, 2,3,K n = 1, 2,3,K T v= v v fn = = n n 2L Speed of a wave in a wire Depends on: 1. linear mass density () = mass/length (kg/m) 2.Tension in string (T) Closed Pipes Have an antinode at one end and a node at the other. Each sound you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound? You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength. This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC. Closed Pipes Harmonics Harmonics are MULTIPLES of the fundamental frequency. In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced Closed Pipes Harmonics In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced. CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS! Closed at one end: v fn = n 4L n = 1,3,5,K Open Pipes OPEN PIPES- have an antinode on BOTH ends of the tube. What is the SMALLEST length of pipe you can have to hear a sound? You will get your FIRST sound when the length of the pipe equals one-half of a wavelength. Open Pipes Harmonics Since harmonics are MULTIPLES of the fundamental, the second harmonic of an "open pipe" will be ONE WAVELENGTH. The picture above is the SECOND harmonic or the FIRST OVERTONE. Open pipes Harmonics Another half of a wavelength would ALSO produce an antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends The picture above is the THIRD harmonic or the SECOND OVERTONE. CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS! STANDING WAVES IN AIR COLUMNS Open at both ends: v fn = n 2L n = 1, 2,3,K Example The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm. v = 2lf 340 = 2(0.675) f f = 251.85 HZ Example The windpipe of a typical whooping crane is about 1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37C. [(0.6)(37)] + 331 = v = 4lf v = 4(1.525) f f = 57.90 Hz 353.2 m/s Example 3 A steel wire in a piano has a length of 0.700 m and a mass of 4.300 103 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical scale)? Example 4 Two pieces of steel wire with identical cross sections have lengths of L and 2L. The wires are each fixed at both ends and stretched so that the tension in the longer wire is four times greater than in the shorter wire. If the fundamental frequency in the shorter wire is 60 Hz, what is the frequency of the second harmonic in the longer wire?
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Special Case Ray DiagramsAP Physics BWhat if the object is ON &quot;f &quot; ?f If the object is ON the focal point, no image is produced as there is NO intersection. fCfPrincipal axisConverging Lens Inside of &quot;f &quot;ffWhen object is inside of &quot;f&quot;, extend th
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Clicker Question ConcepTests PRS-Enabled Chapter 2 Physics, 3rd Edition James S. Walker 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and asse
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Physics 12 Ultimate Electrostatics Assignment Key Formulae:F=k Q1Q2 r2Name:E=F Q V d kQ rE=kQ r2V =EP Q Q1Q2 rE=Ep = k 0108 1.V=2.3.4.0106 5.6.7.8.0101 9.10.11.12.0008 13.14.15.16.0006 17.18.19.20.0001 21.22.23.24.9908 2
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 1: Momentum &amp; ImpulseHow does a karate expert chop through cement blocks with a bare hand? Why does a fall onto a trampoline hurt less than onto a cement floor? Why do people in larger vehicles usually end up with fewer injuries in accidents? It's
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
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Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 9: Coulomb's LawCharles Augustin de CoulombBefore getting into all the hardcore physics that surrounds him, it's a good idea to understand a little about Coulomb. He was born in 1736 in Angoulme, France. He received the majority of his higher edu
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 9: d-t &amp; v-t GraphsGraphing the motion of objects gives us a way to interpret the motion that would otherwise be difficult. Graphs will also allow you to show a large amount of information in a compact way. Essentially you need to be able to sketc
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 10: Electric FieldsJust like the force due to gravity, the force due to electric charges can act over great distances. Keep in mind that most forces we deal with in everyday life are not like this. We mostly deal with &quot;contact forces&quot;. objects tou
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 12: GravityAristotleFrom the time of Aristotle (384-322 BC) until the late 1500's, gravity was believed to act differently on different objects. This was based on Aristotle's observations of doing things like dropping a metal bar and a feather at
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 12: Electric Potential Energy &amp; VoltageGravitational Potential EnergyTo better understand electric potential energy it is a good idea to first review gravitational potentialenergy and figure out similarities between them. Understanding the para
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 13: Vectors in One DimensionUp to this point we have been focusing on the number crunching sort of questions you can do in physics. In this chapter the focus will start to be shifted toward more complicated problems that might notalways be solve
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 13: Voltage in a Uniform FieldMost of the time if we are doing experiments with electric fields, we use parallel plates to ensure thatthe field is uniform (the same everywhere). This carries over to our study of voltage. If we use parallel plate
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 14: Vectors in Two DimensionsTwo dimensional problems are a little tougher, because we are no longer just lining up collinear vectorsand doing quick math. Instead, we need to pay attention to how the vectors form a more complex (but not verycom
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 21: Free Body DiagramsFree Body DiagramsWe will need a way to organize forces that are acting on a particular object. The easiest way to do this isby using a free body diagram. A free body diagram is just a simple sketch of the object showing a
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 22: Net ForceThe net force is the vector sum of all the forces acting on anobject. If the forces are parallel we can just add themtogether as positive and negative forces. If the forces are at an angle we have to add them ascomponents of vect
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 23: Newton's First Law (Inertia)Newtons Laws of Motion, as written in his book the Principia, are actually very difficult to read. At the time, Newton didnt care too much about the readability of his book. He just wanted toget the stuff put down
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 24: Newton's Second Law (Motion)To really appreciate Newtons Laws, it sometimes helps to see how they build on each other. The First Law describes what will happen if there is no force. The Second Law describes what will happen if there is a for
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 25: Newton's Third Law (Action-Reaction)Newton came up with one more law when he started thinking about the interaction of objects. He had already talked about what happens when there is no force (1st Law). He then talked about what happens when
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 26: FrictionFriction is a force that always exists between any two surfaces in contact with each other. There is no such thing as a perfectly frictionless environment. Even in deep space, bits of micrometeorites will hit a moving object, causing
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 27a: Torque (AP Only)Torque BasicsTorque is a concept that is very closely related to the ideas we've been developing about force.Just like force is a push or a pull on an object, torque is aWe will only discuss rigid objects in ourtwist.stud
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 27: Gravity on Inclined PlanesYou need to be especially careful when you are doing problems involving gravity pulling somethingdown a slope. The physics involved is considerably more complex than it might first seem, mostly becauseeverything is
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 29: Newton's Law of Universal GravitationLet's say we start with the classic apple on the head version of Newton's work. Newton started with the idea that since the Earth is pulling on the apple, the apple must also bepulling on the Earth (Newto
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 42a: Kinetic Theory of Ideal GasesThe TheoryThe kinetic theory of ideal gases is one of those rare things in physics. it makes sense!Basically, from the point you started to learn about gases in elementary school, you werelearning about the bas
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 42b: First Law of ThermodynamicsThe First Law of Thermodynamics can be stated in several ways.At this point in the course we need to focus on what it says about energy, and gases in thekinetic theory of ideal gases.We will look at how adding he
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 42c: PV DiagramsFrom the last section, you were probably wondering what happens when we do something like add heatto a sealed cylinder.This sounds like a pretty dangerous idea if you think back to the WHMIS training you hadabout compressed gas
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 42d: Second Law of Thermodynamics &amp; EntropyThe Second Law of ThermodynamicsIf you take a can of Dr Pepper out of the fridge and walk outside on a hot summer day, you expect thedrink to get warmer as time passes. You would never expect it to get
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 54: Fluids (AP Only)FluidsThe word fluid will most often make people think about some kind of liquid. The four states of matterare solid, liquid, gas, andIn physics, fluid can refer to either a gas or a liquid.plasma. Of these four, gasesand
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 55: Archimedes' Principle (AP Only)Archimedes of Syracuse is probably one of the most important scientists andmathematicians of all time.Although he lived over 2200 years ago, he was able to make somefundamental discoveries in the study of phys
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 56: Pressure (AP Only)Although we don't think about it, we live at the bottom of a roughly 100 km deep sea of air.Air is made of molecules, so it has mass. Under the effect of gravity, it quite literally weighsdown on us every single moment of o
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 57: Pascal's Principle (AP Only)Imagine that you have a container of fluid.From what we've ;earned so far, we know that the pressure the fluid exerts on the sides of thecontainer are the same everywhere. If they were not, the fluid would no lon
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 58: Pressure in Static Fluid Columns (AP Only)If you've ever done any deep diving underwater, you'll know about the effects it has on your body.Most people get the basic idea that as you go deeper underwater, the pressure increases. It's whyit i
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 59: Principle of Continuity (AP Only)We've spent a lot of time so far looking at hydrostatics, fluids at rest.Even when we looked at problems with moving fluids (like Pascal's Principle), you would notdescribe the fluid as flowing, like water th
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Lesson 60: Bernoulli's Equation (AP Only)Bernoulli's Equation looks at the pressure at two different locations for a moving fluid.It is really intimidating when you first see it, but it's not as bad as it might look.11P 1 g y 1 v 2= P 2 g y 2 v 212
Aarhus Universitet, Handels- og IngeniørHøjskolen - PHYSICS - 20339841
Momentum &amp; Energy Extra Study QuestionsShort Answer1. What is the momentum of a 1000 kg car moving at 15 m/s [E]?2. Calculate the momentum of each of the following objects.(a) a 0.50 kg ball thrown upward with a velocity of 30 m/s(b) a 2000 kg railwa
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