The Great Wave Hokusai. LO: Recognize physical principles associated with terms in sonar equation.
|
|
- Roderick Harper
- 5 years ago
- Views:
Transcription
1 Sona Equation: The Wave Equation The Geat Wave Hokusai LO: Recognize hysical inciles associated with tems in sona equation.
2 the Punchline If density too high to esolve individual oganisms, then: E[enegy fom volume] n * enegy fom an individual enegy fom individual σ bs backscatteing coss section enegy fom volume s v volume backscatte coefficient So E[s v ] n σ bs - measue enegy fom volume - assume, measue, o model enegy fom eesentative individual - can calculate density of individuals
3 Definitions Wave Numbe: k π/λ (units ad/m) Angula Fequency: ω π/τπf (units ad/s) Pessue (): foce/aea (units Pascals N/m, 1µPa 10-6 Pa) () ( o ) o / Intensity (I): owe/aea (units W/m ) I() I( o ) ( o /) I
4 Hugen s Pincile Evey oint in a wave field acts as a oint souce Intefeence among souces (e.g. iles in a ond) Constuctive Destuctive + +
5 Poagating Waves Am D 1 (x) D (x) x 1 10 D (x) D 1 (x-10) D 1 (x - ms -1 * 5 s) D(x) D 1 (x-ct) Since c λ/t D(x) D 1 (x-λ/t* t) D 1 (x-λft) Make non-dimensional: divide by λ D(x/λ) D 1 (x/λ ft) seed ms -1
6 Non-dimensional Wave Equation Make non-dimensional: divide by λ D(x/λ) D 1 (x/λ ft) Recall π/λ k; πf ω D(k,x) D1(kx - ωt) +x diection D(k,x) D1(kx + ωt) -x diection
7 Hamonic Motion k m x Foce -kx F ma Theefoe: ma -kx m d x dt kx 0 kx m d x dt Divide by m: 0 d x dt + kx m
8 Hamonic Motion x made u of ats: k k x Acos t 1 m x Bsin t m So: k k x Acos + t Bsin t m m x since ω ( ωt) Bsin( ωt) Acos + k m k Units k N/kg (kg/s )/kg s - Squae oot s -1 ad/s ω Sinusoidal fom with magnitude 1 B A B and hase α tan A C + x C cos t ( ω α ) A,B,C comlex constants
9 Altenate Solution fo Hamonic Motion x made u of ats: So: e t i D x ω 1 e t i E x ω e e t i t i E D x ω ω + Wave Equation fo Acoustics 1 c t δ δ Fo lane waves in 1 diection: δx δ 1 c t x δ δ δ δ LaPlacian oeato
10 Plane Wave Incident Solution ( x, t) A e i ( kx t ) i( kx t ) ω +ω + B e fowad Fowad Taveling Plana Wave: evese (x,t) C cos(kx-ωt), whee C is efeence essue ( o ) Altenate fom: e ( k ωt ) o o i x ange
11 Plana Incident Pessue inc o o e i ( k ωt ) t t o t o e i( k ωt)
12 Sheical Scatteing δ δ δ δ + LaPlacian Wave Equation 1 t c δ δ δ δ δ δ + is distance fom souce cente Solution ( ) ( ) e e t k i o o t k i A ω ω amlitude fequency
13 Diectivity: D D( θ ) kl sin sinθ kl sinc sinθ k sinθ L sinc(sin(x)/x)
14 Tansduce Diectivity: D whee: D I o / I o adiated intensity at acoustic axis mean intensity ove all diections Diectivity Index D i D i 10log(D) fom tansduce D i 10 log(4πa/λ) whee a active tansduce aea fom beam angles D i 10log(.5/sin(β 1 /) sin(β /)) whee β s beam width at 3dB oints
15 Tansduce Beam Patten Shading used to fom main lobe though constuctive and destuctive intefeence * sound atten is indeendent of intensity (analogous to flashlight with low batteies)
16 Don t Foget Tansmission Losses Sheical Seading Δ α 1/ ΔI α 1/ I Absotion α/0 α 1/ o 10 log 10 ( 1 / ) I I α/10 α 1/ o 10 log 10 (I 1 /I ) o unit distance
17 Putting Comonents Togethe Pessue () ( o ) o / 10 - α(- o /0) Intensity I() I( o ) ( o /) 10 - α(- o /10)
18 Sona Equation fo Pessue () ( o ) o / 10 - α(- o /0) Divide by efeence essue o ()/ o ( o ) / o o / 10 - α(- o /0) Take 0 log 10 of both sides: 0 log 10 (()/ o ) 0 log 10 (( o ) / o ) + 0 log 10 ( o /) - α(- o )
19 Sona Equation fo Pessue 0 log 10 (()/ o ) 0 log 10 (( o ) / o ) - 0 log 10 ( o /) - α(- o ) SPL SL - TL - TL Sound Pessue Level Echo Level Souce Level Tansmission Losses (one way)
20 Scatteing fom an Object I i Incident sound on taget I Intensity of eflected sound at 1 mete ρ 1 c 1 ρ c TS 10log10 I I i
21 Point o Sheical Scatteing Scatteed Field scat o t o e i ( k ωt ) e ik s t amlitude fequency incident field eflected field s f f comlex scatteing amlitude (a.k.a. comlex scatteing length) eflectivity, taget size, oientation, geomety of tansmit & eceive
22 Acoustic Imedance Scatteing is caused by an Acoustic Imedance mismatch Reflection (1 diection) Scatteing (all diections) i i LARGE objects (e.g. beakwate) small objects (e.g. iling) R / i What is acoustic imedance (Z)? Z ρ c g ρ /ρ 1 h c /c 1 density sound seed
23 g ρ /ρ 1 h c /c gh gh c c c c c c c c R ρ ρ ρ ρ ρ ρ ρ ρ density contast sound seed contast Echoes: Acoustic Imedance Mismatch Reflection
24 Reflection Coefficient ootion of sound eflected at an inteface Incident R w,fb T T R w,fb fb,w fb,sb R fb,sb R eflected T tansmit w wate fb fish body sb swim bladde sb fb R fb, sb g g fb, sb fb, sb h h fb, sb fb, sb 1 + 1
25 Reflectivity Examles Lead in wate g h 1.49 R 14/16 1 Pefect eflecto Ai wate inteface g h 0. R 0-1/0+1-1 Pessue elease suface Atic kill (Euhasia sueba) g h R 0.06/ Atlantic cod (Gadus mohua) Body Swimbladde g g h h 0.3 R R
26 Backscatte Definition f comlex scatteing amlitude (a.k.a. comlex scatteing length) - if f is big then taget scattes lots of sound - backscatte is most common geomety fo a tansduce σ bs backscatteing coss-sectional aea (units m ) TS taget stength (units db e 1 µpa) σ bs bs * bs f f f bs * comlex conjugate TS 10 log ( ) 10 ( σ ) 10 f bs log10 bs
27 Some Final Definitions EL echo level SL souce level 10log 10 ( ) 1µ Pa 10log i i 10 ( ) 1µ Pa (1m ) TL tansmission loss taget (1m ) 10log10 assumes no absotion TS taget stength 10log σ bs (1m ) 10
28 Two Way Scatteing Equation scat 1 1 ( ) σ o o bs taget souce EL SL TL to taget + TL to souce + TS Reaange: TS EL SL + TL (anything missing?)
29 Sona Equation Schematic Tansmit Receive
30 Active vs Passive Systems SPL SL - TL Passive enegy eceived enegy tansmitted * faction not absobed * faction not sead I I o o 10 α 10 o one-way system souce tansmission loss Active SPL ec SL - TL + TS + noise (Σ themal, electical, anthoogenic) two-way system
31 Active vs Passive Alications Passive - detemine how fa away we can hea animals - detemine how fa away animals can hea us (and coesonding intensity level) - detemine ange of animal communication - census oulations - monito behavio Active - detemine how much owe needed to detect animal - detemine ange of edato detecting ey - census and size oulations - ma distibutions of animals
32 Dolhin Sound Recetion Additional Stuctues: Pathway of sound to the cochlea is via the lowe jaw (cf. Bullock et al. 1968; McComick et al. 1970) Nois 1968
The Great Wave Hokusai. LO: Recognize physical principles associated with terms in sonar equation.
Sona Equaion: The Wave Equaion The Gea Wave Hokusai LO: Recognize hysical inciles associaed wih ems in sona equaion. he Punchline If densiy oo high o esolve individual oganisms, hen: E[enegy fom volume]
More information1 Fundamental Solutions to the Wave Equation
1 Fundamental Solutions to the Wave Equation Physical insight in the sound geneation mechanism can be gained by consideing simple analytical solutions to the wave equation. One example is to conside acoustic
More informationChapter 3 Problem Solutions
Chate Poblem Solutions Poblem A Equation (5) gives P P G G log h log h L 4 log d t t t sys Substituting gives P log 6 log log 4 log 875 m B The wavelength is given by 8 The fee-sace ath loss is then 9
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More informationSection 11. Timescales Radiation transport in stars
Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2
More informationChapter 3: Wave propagation fundamentals: From energy point of view, energy partitioning at interfaces
Chapte 3: Wave popagation fundamentals: Fom enegy point of view, enegy patitioning at intefaces Befoe pusuing futhe on discussing specific topics in seismic exploation to a vaiety of applications, it is
More informationCHAPTER IV RADIATION BY SIMPLE ACOUSTIC SOURCE. or by vibratory forces acting directly on the fluid, or by the violent motion of the fluid itself.
CHAPTER IV RADIATION BY SIMPLE ACOUSTIC SOURCE 4.1 POINT SOURCE Sound waves ae geneated by the vibation of any solid body in contact with the fluid medium o by vibatoy foces acting diectly on the fluid,
More informationPhys101 Lectures 30, 31. Wave Motion
Phys0 Lectues 30, 3 Wave Motion Key points: Types of Waves: Tansvese and Longitudinal Mathematical Repesentation of a Taveling Wave The Pinciple of Supeposition Standing Waves; Resonance Ref: -7,8,9,0,,6,,3,6.
More informationTRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the
Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection
More informationB. Spherical Wave Propagation
11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We
More informationDoppler Radar (Fig. 3.1) A simplified block diagram 10/29-11/11/2013 METR
Review Dopple Rada (Fig. 3.1) A simplified block diagam 10/9-11/11/013 METR 5004 1 A ( θϕ, ) exp ψt c i Ei = j π f t + j E A ( θϕ, ) = exp jπ f t + jψt c 4π Vi = Aiexp jπ ft j + jψt λ jq(t) ψ e Complex
More informationApplications of radars: Sensing of clouds and precipitation.
Lectue 1 Applications of adas: Sensing of clouds and pecipitation. Ojectives: 1. aticle ackscatteing and ada equation.. Sensing of pecipitation and clouds with adas (weathe adas, space adas: TMM and CloudSat).
More informationEKT 345 MICROWAVE ENGINEERING CHAPTER 2: PLANAR TRANSMISSION LINES
EKT 345 MICROWAVE ENGINEERING CHAPTER : PLANAR TRANSMISSION LINES 1 Tansmission Lines A device used to tansfe enegy fom one point to anothe point efficiently Efficiently minimum loss, eflection and close
More informationClass XII - Physics Wave Optics Chapter-wise Problems. Chapter 10
Class XII - Physics Wave Optics Chapte-wise Poblems Answes Chapte (c) (a) 3 (a) 4 (c) 5 (d) 6 (a), (b), (d) 7 (b), (d) 8 (a), (b) 9 (a), (b) Yes Spheical Spheical with huge adius as compaed to the eath
More information1.2 Differential cross section
.2. DIFFERENTIAL CROSS SECTION Febuay 9, 205 Lectue VIII.2 Diffeential coss section We found that the solution to the Schodinge equation has the fom e ik x ψ 2π 3/2 fk, k + e ik x and that fk, k = 2 m
More information3. Electromagnetic Waves II
Lectue 3 - Electomagnetic Waves II 9 3. Electomagnetic Waves II Last time, we discussed the following. 1. The popagation of an EM wave though a macoscopic media: We discussed how the wave inteacts with
More informationIntroduction to Arrays
Intoduction to Aays Page 1 Intoduction to Aays The antennas we have studied so fa have vey low diectivity / gain. While this is good fo boadcast applications (whee we want unifom coveage), thee ae cases
More informationCartesian Coordinate System and Vectors
Catesian Coodinate System and Vectos Coodinate System Coodinate system: used to descibe the position of a point in space and consists of 1. An oigin as the efeence point 2. A set of coodinate axes with
More informationII. MRI Technology. B. Localized Information. Lorenz Mitschang Physikalisch-Technische Bundesanstalt, 29 th June 2009
Magnetic Resonance Imaging II. MRI Technology A. Limitations to patial Infomation B. Localized Infomation Loenz Mitschang Physikalisch-Technische Bundesanstalt, www.ptb.de 9 th June 009 A. Limitations
More informationMultipole Radiation. February 29, The electromagnetic field of an isolated, oscillating source
Multipole Radiation Febuay 29, 26 The electomagnetic field of an isolated, oscillating souce Conside a localized, oscillating souce, located in othewise empty space. We know that the solution fo the vecto
More informationRoger Pynn. Basic Introduction to Small Angle Scattering
by Roge Pynn Basic Intoduction to Small Angle Scatteing We Measue Neutons Scatteed fom a Sample Φ = numbe of incident neutons pe cm pe second σ = total numbe of neutons scatteed pe second / Φ dσ numbe
More informationPolar Coordinates. a) (2; 30 ) b) (5; 120 ) c) (6; 270 ) d) (9; 330 ) e) (4; 45 )
Pola Coodinates We now intoduce anothe method of labelling oints in a lane. We stat by xing a oint in the lane. It is called the ole. A standad choice fo the ole is the oigin (0; 0) fo the Catezian coodinate
More informationkg 2 ) 1.9!10 27 kg = Gm 1
Section 6.1: Newtonian Gavitation Tutoial 1 Pactice, page 93 1. Given: 1.0 10 0 kg; m 3.0 10 0 kg;. 10 9 N; G 6.67 10 11 N m /kg Requied: Analysis: G m ; G m G m Solution: G m N m 6.67!10 11 kg ) 1.0!100
More informationBlack Body Radiation and Radiometric Parameters:
Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo
More information, and the curve BC is symmetrical. Find also the horizontal force in x-direction on one side of the body. h C
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Dynamics (Stömningsläa), 2013-05-31, kl 9.00-15.00 jälpmedel: Students may use any book including the textbook Lectues on Fluid Dynamics.
More informationEKT 356 MICROWAVE COMMUNICATIONS CHAPTER 2: PLANAR TRANSMISSION LINES
EKT 356 MICROWAVE COMMUNICATIONS CHAPTER : PLANAR TRANSMISSION LINES 1 Tansmission Lines A device used to tansfe enegy fom one point to anothe point efficiently Efficiently minimum loss, eflection and
More informationPhysics 2212 GH Quiz #2 Solutions Spring 2016
Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying
More informationThe nature of electromagnetic radiation.
Lectue 3 The natue of electomagnetic adiation. Objectives: 1. Basic intoduction to the electomagnetic field: Definitions Dual natue of electomagnetic adiation lectomagnetic spectum. Main adiometic quantities:
More informationMath Section 4.2 Radians, Arc Length, and Area of a Sector
Math 1330 - Section 4. Radians, Ac Length, and Aea of a Secto The wod tigonomety comes fom two Geek oots, tigonon, meaning having thee sides, and mete, meaning measue. We have aleady defined the six basic
More informationX-ray Diffraction beyond the Kinematical Approximation
X-ay Diffaction beyond the Kinematical Appoximation Dynamical theoy of diffaction Inteaction of wave fields X-ays neutons electons with a egula lattice atomic cystal stuctues nanomete scaled multi-layes
More information11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.
Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings
More informationWaves and Polarization in General
Waves and Polaization in Geneal Wave means a distubance in a medium that tavels. Fo light, the medium is the electomagnetic field, which can exist in vacuum. The tavel pat defines a diection. The distubance
More informationOutline. Basics of interference Types of interferometers. Finite impulse response Infinite impulse response Conservation of energy in beam splitters
ntefeometes lectue C 566 Adv. Optics Lab Outline Basics of intefeence Tpes of intefeometes Amplitude division Finite impulse esponse nfinite impulse esponse Consevation of eneg in beam splittes Wavefont
More informationTELE4652 Mobile and Satellite Communications
Mobile and Satellite Communications Lectue 3 Radio Channel Modelling Channel Models If one was to walk away fom a base station, and measue the powe level eceived, a plot would like this: Channel Models
More informationCircular Motion. Mr. Velazquez AP/Honors Physics
Cicula Motion M. Velazquez AP/Honos Physics Objects in Cicula Motion Accoding to Newton s Laws, if no foce acts on an object, it will move with constant speed in a constant diection. Theefoe, if an object
More informationQualifying Examination Electricity and Magnetism Solutions January 12, 2006
1 Qualifying Examination Electicity and Magnetism Solutions Januay 12, 2006 PROBLEM EA. a. Fist, we conside a unit length of cylinde to find the elationship between the total chage pe unit length λ and
More informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity
More informationPhysics 1C Fall 2011: Quiz 1 Version A 1
Physics 1C Fall 2011: Quiz 1 Vesion A 1 Depatment of Physics Physics 1C Fall Quate - 2011 D. Mak Paddock INSTRUCTIONS: 1. Pint you full name below LAST NAME FIRST NAME MIDDLE INITIAL 2. You code numbe
More informationThe condition for maximum intensity by the transmitted light in a plane parallel air film is. For an air film, μ = 1. (2-1)
hapte Two Faby--Peot ntefeomete A Faby-Peot intefeomete consists of two plane paallel glass plates A and B, sepaated by a distance d. The inne sufaces of these plates ae optically plane and thinly silveed
More informationAdvanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet
Advanced Subsidiay GCE (H57) Advanced GCE (H557) Physics B (Advancing Physics) Data, Fomulae and Relationships Booklet The infomation in this booklet is fo the use of candidates following the Advanced
More informationVelocimetry Techniques and Instrumentation
AeE 344 Lectue Notes Lectue # 05: elocimety Techniques and Instumentation D. Hui Hu Depatment of Aeospace Engineeing Iowa State Univesity Ames, Iowa 500, U.S.A Methods to Measue Local Flow elocity - Mechanical
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More information1 2 U CV. K dq I dt J nqv d J V IR P VI
o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C
More informationWave Incidence. Dr. Cruz-Pol. Normal Incidence. Ex.1. Light traveling in air encounters the water; another medium.
D. Cu-Pol Ex.1. Light taveling in ai encountes the wate; anothe medium. Wave Incidence [Chapte 10 cont, Sadiku] D. Sanda Cu-Pol Electical and Compute Engineeing Dept. UPR-Maagüe Ex.1. Light encountes atmosphee,
More informatione.g: If A = i 2 j + k then find A. A = Ax 2 + Ay 2 + Az 2 = ( 2) = 6
MOTION IN A PLANE 1. Scala Quantities Physical quantities that have only magnitude and no diection ae called scala quantities o scalas. e.g. Mass, time, speed etc. 2. Vecto Quantities Physical quantities
More informationc( 1) c(0) c(1) Note z 1 represents a unit interval delay Figure 85 3 Transmit equalizer functional model
Relace 85.8.3.2 with the following: 85.8.3.2 Tansmitted outut wavefom The 40GBASE-CR4 and 100GBASE-CR10 tansmit function includes ogammable equalization to comensate fo the fequency-deendent loss of the
More informationChapter 16. Fraunhofer Diffraction
Chapte 6. Faunhofe Diffaction Faunhofe Appoimation Faunhofe Appoimation ( ) ( ) ( ) ( ) ( ) λ d d jk U j U ep,, Hugens-Fesnel Pinciple Faunhofe Appoimation : ( ) ( ) ( ) λ π λ d d j U j e e U k j jk ep,,
More information2.5 The Quarter-Wave Transformer
/3/5 _5 The Quate Wave Tansfome /.5 The Quate-Wave Tansfome Reading Assignment: pp. 73-76 By now you ve noticed that a quate-wave length of tansmission line ( λ 4, β π ) appeas often in micowave engineeing
More information7.2.1 Basic relations for Torsion of Circular Members
Section 7. 7. osion In this section, the geomety to be consideed is that of a long slende cicula ba and the load is one which twists the ba. Such poblems ae impotant in the analysis of twisting components,
More information2. Radiation Field Basics I. Specific Intensity
. Raiation Fiel Basics Rutten:. Basic efinitions of intensity, flux Enegy ensity, aiation pessue E Specific ntensity t Pencil beam of aiation at position, iection n, caying enegy E, pasg though aea, between
More informationΦ E = E A E A = p212c22: 1
Chapte : Gauss s Law Gauss s Law is an altenative fomulation of the elation between an electic field and the souces of that field in tems of electic flux. lectic Flux Φ though an aea A ~ Numbe of Field
More informationECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 4
ECE 6340 Intemediate EM Waves Fall 016 Pof. David R. Jackson Dept. of ECE Notes 4 1 Debye Model This model explains molecula effects. y We conside an electic field applied in the x diection. Molecule:
More informationA moving charged particle creates a magnetic field vector at every point in space except at its position.
1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More informationF g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N
Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the
More informationSubstances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.
Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed
More informationME 3600 Control Systems Frequency Domain Analysis
ME 3600 Contol Systems Fequency Domain Analysis The fequency esponse of a system is defined as the steady-state esponse of the system to a sinusoidal (hamonic) input. Fo linea systems, the esulting steady-state
More informationAH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion
AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed
More informationFri Angular Momentum Quiz 10 RE 11.a; HW10: 13*, 21, 30, 39 Mon , (.12) Rotational + Translational RE 11.b Tues.
Fi. 11.1 Angula Momentum Quiz 10 R 11.a; HW10: 13*, 1, 30, 39 Mon. 11.-.3, (.1) Rotational + Tanslational R 11.b Tues. P10 Mon. 11.4-.6, (.13) Angula Momentum & Toque Tues. Wed. 11.7 -.9, (.11) Toque R
More informationPhys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
More informationKCET 2015 TEST PAPER WITH ANSWER KEY (HELD ON TUESDAY 12 th MAY, 2015) MATHEMATICS ALLEN Y (0, 14) (4) 14x + 5y ³ 70 y ³ 14and x - y ³ 5 (2) (3) (4)
KET 0 TEST PAPER WITH ANSWER KEY (HELD ON TUESDAY th MAY, 0). If a and b ae the oots of a + b = 0, then a +b is equal to a b () a b a b () a + b Ans:. If the nd and th tems of G.P. ae and esectively, then
More informationPHYS 2135 Exam I February 13, 2018
Exam Total /200 PHYS 2135 Exam I Febuay 13, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each Choose the best o most nealy coect answe Fo questions 6-9, solutions must begin
More information( ) Make-up Tests. From Last Time. Electric Field Flux. o The Electric Field Flux through a bit of area is
Mon., 3/23 Wed., 3/25 Thus., 3/26 Fi., 3/27 Mon., 3/30 Tues., 3/31 21.4-6 Using Gauss s & nto to Ampee s 21.7-9 Maxwell s, Gauss s, and Ampee s Quiz Ch 21, Lab 9 Ampee s Law (wite up) 22.1-2,10 nto to
More informationSolution Set #3
05-733-009 Solution Set #3. Assume that the esolution limit of the eye is acminute. At what distance can the eye see a black cicle of diamete 6" on a white backgound? One acminute is, so conside a tiangle
More informationb) (5) What average force magnitude was applied by the students working together?
Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults
More informationElectromagnetic Properties of Materials Part I
9/19/16 ECE 53 1 st Centuy Electomagnetics Instucto: Office: Phone: E Mail: D. Raymond C. Rumf A 337 (915) 747 6958 cumf@ute.edu Lectue # Electomagnetic Poeties of Mateials Pat I Loentz and Dude Models
More informationChapter 31 Faraday s Law
Chapte 31 Faaday s Law Change oving --> cuent --> agnetic field (static cuent --> static agnetic field) The souce of agnetic fields is cuent. The souce of electic fields is chage (electic onopole). Altenating
More informationFaraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law
Faaday s Law Faaday s Epeiments Chapte 3 Law of nduction (emf( emf) Faaday s Law Magnetic Flu Lenz s Law Geneatos nduced Electic fields Michael Faaday discoeed induction in 83 Moing the magnet induces
More informationA 1. EN2210: Continuum Mechanics. Homework 7: Fluid Mechanics Solutions
EN10: Continuum Mechanics Homewok 7: Fluid Mechanics Solutions School of Engineeing Bown Univesity 1. An ideal fluid with mass density ρ flows with velocity v 0 though a cylindical tube with cosssectional
More informationr r q Coulomb s law: F =. Electric field created by a charge q: E = = enclosed Gauss s law (electric flux through a closed surface): E ds σ ε0
Q E ds = enclosed ε S 0 08 Fomulae Sheet 1 q 1q q Coulomb s law: F =. Electic field ceated by a chage q: E = 4πε 4πε Pemittivity of fee space: 0 1 = 9 10 4πε 0 9 Newton mete / coulomb = 9 10 9 0 N m Q
More information1) Consider an object of a parabolic shape with rotational symmetry z
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Mechanics (Stömningsläa), 01-06-01, kl 9.00-15.00 jälpmedel: Students may use any book including the tetbook Lectues on Fluid Dynamics.
More information16.1 Permanent magnets
Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationFields and Waves I Spring 2005 Homework 8. Due: 3 May 2005
Fields and Waves I Sping 005 Homewok 8 Tansmission Lines Due: 3 May 005. Multiple Choice (6) a) The SWR (standing wave atio): a) is a measue of the match between the souce impedance and line impedance
More informationObservation of Coherent OTR at LCLS. Unexpected Physics in Standard Beam Diagnostics
Obsevation of Coheent OTR at LCLS Unexpected Physics in Standad Beam Diagnostics 16 Novembe 7 Theoy Goup Meeting Henik Loos loos@slac.stanfod.edu Outline Intoduction into LCLS Injecto Coheent OTR Obsevations
More informationAnalysis of Finite Word-Length Effects
T-6.46 Digital Signal Pocessing and Filteing 8.9.4 Intoduction Analysis of Finite Wod-Length Effects Finite wodlength effects ae caused by: Quantization of the filte coefficients ounding / tuncation of
More informationBroadband Noise Predictions Based on a New Aeroacoustic Formulation
Boadband Noise Pedictions Based on a New Aeoacoustic Fomulation J. Caspe and F. Faassat NASA Langley Reseach Cente Hampton, Viginia AIAA Pape -8 Aifame Noise Session 4 th AIAA Aeospace Sciences Meeting
More informationPART- A 1. (C) 2. (D) 3. (D) 4. (B) 5. (D) 6. (C) 7. (D) 8. (B) 9. (D) 10. (B) 11. (B) 12. (B) 13. (A) 14. (D)
PRACTICE TEST-4 KISHORE VAIGYANIK PROTSAHAN YOJANA (KVPY) 7 STREAM (SA)_ DATE : -9-7 ANSWER KEY PART- A. (C). (D) 3. (D) 4. (B) 5. (D) 6. (C) 7. (D) 8. (B) 9. (D). (B). (B). (B) 3. (A) 4. (D) 5. (C) 6.
More informationPY208 Matter & Interactions Final Exam S2005
PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula
More informationPROBLEM SET 5. SOLUTIONS March 16, 2004
Havad-MIT ivision of Health Sciences and Technology HST.54J: Quantitative Physiology: Ogan Tanspot Systems Instuctos: Roge Mak and Jose Venegas MASSACHUSETTS INSTITUTE OF TECHNOLOGY epatments of Electical
More informationDepartment of Chemistry Chapter 4 continued
Chapte 4 continued Chial o not chial esponse functions otational aveages linea and nonlinea signals Undestanding this And maybe this Non-linea signal signal ( ( ( ( f E( tn sf... E( t2 q E( t 0q aveage
More informationANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. D = εe. For a linear, homogeneous, isotropic medium µ and ε are contant.
ANTNNAS Vecto and Scala Potentials Maxwell's quations jωb J + jωd D ρ B (M) (M) (M3) (M4) D ε B Fo a linea, homogeneous, isotopic medium and ε ae contant. Since B, thee exists a vecto A such that B A and
More informationWater Tunnel Experiment MAE 171A/175A. Objective:
Wate Tunnel Expeiment MAE 7A/75A Objective: Measuement of te Dag Coefficient of a Cylinde Measuement Tecniques Pessue Distibution on Cylinde Dag fom Momentum Loss Measued in Wake it lase Dopple Velocimety
More informationCollaborative ASSIGNMENT Assignment 3: Sources of magnetic fields Solution
Electicity and Magnetism: PHY-04. 11 Novembe, 014 Collaboative ASSIGNMENT Assignment 3: Souces of magnetic fields Solution 1. a A conducto in the shape of a squae loop of edge length l m caies a cuent
More informationGraphs of Sine and Cosine Functions
Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the
More informationInverse Square Law and Polarization
Invese Squae Law and Polaization Objectives: To show that light intensity is invesely popotional to the squae of the distance fom a point light souce and to show that the intensity of the light tansmitted
More informationAnalysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic
In the fixed-oint imlementation of a digital filte only the esult of the multilication oeation is quantied The eesentation of a actical multilie with the quantie at its outut is shown below u v Q ^v The
More informationLecture 2 Date:
Lectue 2 Date: 5.1.217 Definition of Some TL Paametes Examples of Tansmission Lines Tansmission Lines (contd.) Fo a lossless tansmission line the second ode diffeential equation fo phasos ae: LC 2 d I
More informationTutorial Exercises: Central Forces
Tutoial Execises: Cental Foces. Tuning Points fo the Keple potential (a) Wite down the two fist integals fo cental motion in the Keple potential V () = µm/ using J fo the angula momentum and E fo the total
More informationSection 26 The Laws of Rotational Motion
Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to
More informationPHYS 1410, 11 Nov 2015, 12:30pm.
PHYS 40, Nov 205, 2:30pm. A B = AB cos φ x = x 0 + v x0 t + a 2 xt 2 a ad = v2 2 m(v2 2 v) 2 θ = θ 0 + ω 0 t + 2 αt2 L = p fs µ s n 0 + αt K = 2 Iω2 cm = m +m 2 2 +... m +m 2 +... p = m v and L = I ω ω
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationSolutions. V in = ρ 0. r 2 + a r 2 + b, where a and b are constants. The potential at the center of the atom has to be finite, so a = 0. r 2 + b.
Solutions. Plum Pudding Model (a) Find the coesponding electostatic potential inside and outside the atom. Fo R The solution can be found by integating twice, 2 V in = ρ 0 ε 0. V in = ρ 0 6ε 0 2 + a 2
More informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),
More informationPhysics 1114: Unit 5 Hand-out Homework (Answers)
Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),
More informationGM r. v = For Newton s third law, the forces in the action/reaction pair always act on different objects
SAT Physics Mechanics The dot poduct of two vectos: A B = AB cos θ The coss poduct of vectos: A B = AB sin θˆn. The magnitude of the coss poduct is equal to the aea of the paallelogam. We use the ight
More information1. A stone falls from a platform 18 m high. When will it hit the ground? (a) 1.74 s (b) 1.83 s (c) 1.92 s (d) 2.01 s
1. A stone falls fom a platfom 18 m high. When will it hit the gound? (a) 1.74 s (b) 1.83 s (c) 1.9 s (d).01 s Constant acceleation D = v 0 t + ½ a t. Which, if any, of these foces causes the otation of
More informationSuperposition. Section 8.5.3
Supeposition Section 8.5.3 Simple Potential Flows Most complex potential (invicid, iotational) flows can be modeled using a combination of simple potential flows The simple flows used ae: Unifom flows
More information/6/4 5 Stuctue-Induced Sediment Scou ef: Eosion and Sedimentation, P.Y. Julien, 998 The Mechanics of Scou in the Maine Envionment, B.M. Sume and J. Fedsoe, Evaluating Scou at Bidges (HEC-8), E.. ichadson
More information