DOCSLIB.ORG

Pre-AP Physics – Chapter 12 Notes – Yockers – JHS 2006

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Pre-AP Physics – Chapter 12 Notes – Yockers – JHS 2006 Pre-AP Physics – Chapter 14 Notes – Yockers Vibrations and Waves Hooke’s Law Fs kx →Fs = force of a spring (may be referred to as a “restoring force”) →k = spring constant (reflects the stiffness of the spring) →x = displacement (x = 0 is the equilibrium position) - the direction of the restoring force (Fs) is such that the object is being either pushed or pulled toward the equilibrium position - what is the description of an object’s motion in a system governed by Hooke’s law? →Fs →v and p →a - simple harmonic motion occurs when the net force along the direction of motion is a Hooke’s law type of force – that is, when the net force is proportional to the displacement and in the opposite direction - the energy stored in a stretched or compressed spring or other elastic material is called elastic potential energy (PEs) 1 PE kx 2 s 2 - energy is stored in a spring only when it is either stretched or compressed - the elastic potential energy is a maximum when a spring has reached its maximum compression or extension - PEs is always positive Simple Pendulum - restoring force is a component of the bob’s weight - the motion of a pendulum is not SHM - if the angular displacement from equilibrium is small (less than about 15 degrees, so sin=) then a pendulum follows the general equation form of Hooke’s law, and it is justified to say there is SHM Amplitude, Period, and Frequency - amplitude (A) ≡ the magnitude of the maximum position of the object relative to its equilibrium position - period (T) ≡ the time required for one complete vibration (one complete cycle of motion) - frequency (f) ≡ the number of vibrations (oscillations) per second (also the inverse of T) →SI unit of frequency is the Hz or s-1 1 1 f or T T f - the period of a pendulum is given by L T 2 g →L = fixed length of the pendulum →g = the acceleration due to gravity (not necessarily the Earth’s!) →period does not depend upon the mass of the bob →period does not depend upon amplitude - how can a time piece using a pendulum be adjusted if it runs fast/slow? - the period (T) of a shadow of an object moving with uniform circular motion is equivalent to the horizontal motion of an object on the end of a spring, so m T 2 k →period depends upon the mass of the oscillating object and the stiffness of the spring →period does not depend upon amplitude of the oscillation Properties of Waves - wave – motion of a disturbance - medium – material through which a disturbance travels →particles within a wave vibrate around an equilibrium position, and changes in their vibration allow the net disturbance to travel from one location to another →mediums – air, water, ground …. →each point in a medium can be treated as a simple harmonic oscillator vibrating with the same frequency as the disturbance causing the wave - a mechanical wave’s propagation requires the existence of a medium (electromagnetic waves do not require a medium) - wave types →pulse – a single nonperiodic disturbance →periodic – source is some form of periodic motion - sine waves describe particles vibrating with simple harmonic motion - transverse wave – particles vibrate perpendicularly to the direction of wave motion →crest, trough →wavelength () – distance between two adjacent similar points of the wave - longitudinal wave – particles vibrate parallel to the direction of wave motion →can also be described by a sine wave - density wave or - pressure wave - superposition – displacement is algebraic sum of displacements of individual wave pulses Period, Frequency, and Wave Speed - when vibrating particles of a medium complete one full cycle, one complete wavelength passes any given point - frequency describes the number of crests that pass a given point in a unit of time - period is the amount of time required for one complete vibration of the particles of the medium - speed of a wave x v t v f T - the speed of a wave changes only when the waves move from one medium to another or when properties of the medium are changed Wave Interference - superposition principle – if two or more traveling waves are moving through a medium, the resultant wave is found by adding together the displacements of the individual waves point by point) - constructive interference – when waves meet crest to crest and trough to trough, the superposition principle results in a greater amplitude/displacement - destructive interference – when waves meet crest to trough, the superposition principle results in a smaller amplitude/displacement Reflection - whenever a traveling wave reaches a boundary between mediums, part or all of the wave is reflected - "fixed" reflection – reflection of a pulse traveling on string that is fixed at one end →pulse is inverted →string exerts an upward force, wall exerts a downward force →this downward force causes the pulse to be inverted when reflected - "open" reflection – reflection of a pulse traveling on a string that is attached to a ring of negligible mass that is free to slide along a post without friction →pulse is not inverted →upon reaching the post, the pulse exerts a force on the ring →the ring accelerates upward →ring returns to its original position by the downward component of the tension - when a pulse reaches a boundary, it is partly reflected and partly transmitted past the boundary into the new medium Standing Waves - standing wave – wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere (wavelengths that do not allow both ends to be nodes do not produce standing waves) - standing waves can be set up in a stretched spring by fixing one end to a stationary object and connecting the other end to a vibrating object →traveling waves reflect from the fixed end, creating waves traveling in both directions →the incident and reflected waves combine according to the superposition principle →if the string is vibrated at the right frequency, the wave appears to stand still - node – occurs where the two traveling waves always have the same magnitude of displacement but have opposite sign, so that the net displacement is zero at that point (“no motion”) - antinode – midway between nodes, where the string vibrates with the largest amplitude - all points on the string oscillate together vertically with the same frequency but that different points have different amplitudes of motion →nodes are stationary, and the points at which the string is attached to the →stationary object and vibrating object are also nodes →the distance between nodes is equal to one half of the wavelength of the wave 1 d NN 2 .
Load more

Recommended publications
  • Part II-1 Water Wave Mechanics
    Chapter 1 EM 1110-2-1100 WATER WAVE MECHANICS (Part II) 1 August 2008 (Change 2) Table of Contents Page II-1-1. Introduction ............................................................II-1-1 II-1-2. Regular Waves .........................................................II-1-3 a. Introduction ...........................................................II-1-3 b. Definition of wave parameters .............................................II-1-4 c. Linear wave theory ......................................................II-1-5 (1) Introduction .......................................................II-1-5 (2) Wave celerity, length, and period.......................................II-1-6 (3) The sinusoidal wave profile...........................................II-1-9 (4) Some useful functions ...............................................II-1-9 (5) Local fluid velocities and accelerations .................................II-1-12 (6) Water particle displacements .........................................II-1-13 (7) Subsurface pressure ................................................II-1-21 (8) Group velocity ....................................................II-1-22 (9) Wave energy and power.............................................II-1-26 (10)Summary of linear wave theory.......................................II-1-29 d. Nonlinear wave theories .................................................II-1-30 (1) Introduction ......................................................II-1-30 (2) Stokes finite-amplitude wave theory ...................................II-1-32
    [Show full text]
  • Surface Waves NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU Outline
    Surface Waves NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU Outline – Surface winds • Wind stress • Beaufort scale • Buoy measurements – Surface Gravity Waves • Wave characteristics • Deep/Shallow water waves • Generation • Modeling January mean atmospheric circulation and surface winds Fig 2.3 Ocean Circulation July mean atmospheric circulation and surface winds Fig 2.3 Ocean Circulation Wind Forcing at the Ocean Surface • Wind-forcing can generate currents and waves, as wind transfers some of its momentum into the ocean" •! Wind acts via friction at the surface: wind stress τ# " # # Stresses have units of N/m2, (force/area), like pressure.# Stresses are forces parallel to a surface, pressure is force perpendicular to the surface." •! Force/Area depends on the square of the wind speed u, and it points in the same direction as the wind: " 2 τ ∝ u C drag coefficient 1.4 10−3 " D = ≈ × C u u 3 τ = ρa D density of air 1.3 kg / m " ρa = ≈ Example: 20kt wind $ 10 m/s → 0.18 N/m2 = 1.8 dyne/cm2" 0, <1 knot 1, 1-3 knots 2, 4-6 knots 3, 7-10 knots 4, 11-17 knots 5, 17-21 knots 6, 22-27 knots 7, 28-33 knots 8, 33-40 knots 9, 41-47 knots 10, 48-55 knots 11, 56-63 knots Beaufort scale, after http://www.geology.wmich.edu/Kominz/windwater.html Beaufort scale still provides climatological data Look at buoy winds off oregon coast. http://www.wrh.noaa.gov/pqr/ Outline –! Surface winds •! Wind stress •! Beaufort scale •! Buoy measurements –! Surface Gravity Waves •! Wave characteristics •! Deep/Shallow water waves •! Generation •! Modeling Wave Propagation • Wave Period T: time between arrival of successive wave crests at a given place • Wave Length L: distance between successive wave crests • Wave (phase) speed c: cp = L / T By definition, the definition of cp is valid for all Segar waves.
    [Show full text]
  • On the Transport of Energy in Water Waves
    On The Transport Of Energy in Water Waves Marshall P. Tulin Professor Emeritus, UCSB [email protected] Abstract Theory is developed and utilized for the calculation of the separate transport of kinetic, gravity potential, and surface tension energies within sinusoidal surface waves in water of arbitrary depth. In Section 1 it is shown that each of these three types of energy constituting the wave travel at different speeds, and that the group velocity, cg, is the energy weighted average of these speeds, depth and time averaged in the case of the kinetic energy. It is shown that the time averaged kinetic energy travels at every depth horizontally either with (deep water), or faster than the wave itself, and that the propagation of a sinusoidal wave is made possible by the vertical transport of kinetic energy to the free surface, where it provides the oscillating balance in surface energy just necessary to allow the propagation of the wave. The propagation speed along the surface of the gravity potential energy is null, while the surface tension energy travels forward along the wave surface everywhere at twice the wave velocity, c. The flux of kinetic energy when viewed traveling with a wave provides a pattern of steady flux lines which originate and end on the free surface after making vertical excursions into the wave, even to the bottom, and these are calculated. The pictures produced in this way provide immediate insight into the basic mechanisms of wave motion. In Section 2 the modulated gravity wave is considered in deep water and the balance of terms involved in the propagation of the energy in the wave group is determined; it is shown again that vertical transport of kinetic energy to the surface is fundamental in allowing the propagation of the modulation, and in determining the well known speed of the modulation envelope, cg.
    [Show full text]
  • Experimental Study of Water Waves: Nonlinear Effects and Absorption
    Experimental study of water waves : nonlinear effects and absorption Eduardo Monsalve Gutierrez To cite this version: Eduardo Monsalve Gutierrez. Experimental study of water waves : nonlinear effects and absorp- tion. Mechanics [physics]. Université Pierre et Marie Curie - Paris VI, 2017. English. NNT : 2017PA066027. tel-01589016 HAL Id: tel-01589016 https://tel.archives-ouvertes.fr/tel-01589016 Submitted on 18 Sep 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Université Pierre et Marie Curie Ecole doctorale 391: Sciences mécaniques, acoustique, électronique et robotique de Paris Laboratoire de Physique et Mécanique des Milieux Hétérogènes / Groupe MOndeS Études expérimentales des ondes à la surface de l'eau: effets non linéaires et absorption. Experimental study of water waves: nonlinear effects and absorption. Par Eduardo Monsalve Gutiérrez Thèse de doctorat de dynamique des fluides et des transferts Dirigée par Agnès MAUREL, Vincent PAGNEUX & Philippe PETITJEANS Présentée et soutenue publiquement le 20 mars 2017 Devant un jury composé de : M. Sébastien Guenneau, Directeur de Recherche au CNRS Rapporteur M. Michel Benoit, Professeur IRPHE & Ecole Centrale Marseille Rapporteur M. Christophe Josserand, Directeur de Recherche au CNRS Président du jury Mme. Agnès Maurel, Directrice de Recherche au CNRS Co-directrice de thèse M.
    [Show full text]
  • Ch 14 Lecture Hand
    Chapter 14 Overview 13.7 Waves 14.5 Spherical and Plane Waves 13.8 Frequency, Amplitude, and Wavelength 14.6 The Doppler Effect 13.9 The Speed of Waves on 14.7 Interference of Sound Strings Waves 13.10 Interference of Waves 14.8 Standing Waves 13.11 Reflection of Waves 14.9 Forced Vibrations and Resonance 14.1 Producing a Sound Wave 14.10 Standing Waves in Air 14.2 Characteristics of Sound Columns Waves 14.11 Beats 14.3 The Speed of Sound 14.12 Quality of Sound 14.4 Energy and Intensity of Sound Waves Definitions Definitions Pulse – one wave bump Amplitude – maximum distance the wave moves above or below the equilibrium point Traveling wave – moving pulse Crest – peak of wave Medium – matter that wave travels through Trough – bottom of wave Transverse wave – particles move perpendicular to wave velocity Wavelength – the desistance from two successive points on a wave (crest to crest) Longitudinal wave – particles of medium move parallel to direction of wave motion Wave speed – speed that a certain part of the wave (crest) Mechanical wave – requires matter (medium) moves through the medium Equation Speed of a Wave Superposition Principle v = fλ When two or more traveling waves encounter each other while moving through a medium, the resultant wave is found by Where v is wave speed, f is frequency, and λ is wavelength adding together the displacements of the individual waves point by point. Definitions Reflection of Waves Constructive interference – waves FIXED END (HARD BOUNDARY) FREE END (LOOSE BOUNDARY) that overlap in phase, or crest to crest and trough to trough Destructive interference – waves that overlap 180° out of phase, or crest to trough and trough to crest Making Connections The speaker (and the particles of air) acts like mass-spring systems in SHM.
    [Show full text]
  • Nondirectional and Directional Wave Data Analysis Procedures
    NDBC Technical Document 96-01 Nondirectional and Directional Wave Data Analysis Procedures Stennis Space Center January 1996 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Data Buoy Center 96-002(1) 96-002(1) NDBC Technical Document 96-01 Nondirectional and Directional Wave Data Analysis Procedures Marshall D. Earle, Neptune Sciences, Inc. 150 Cleveland Avenue, Slidell, Louisiana 70458 January 1996 U.S. DEPARTMENT OF COMMERCE Ronald Brown, Secretary National Oceanic and Atmospheric Administration Dr. D. James Baker National Data Buoy Center Jerry C. McCall, Director 96-002(1) 96-002(1) TABLE OF CONTENTS PAGE 1.0 INTRODUCTION .......................................................... 1 2.0 PURPOSE ............................................................... 1 3.0 DATA ANALYSIS PROCEDURES ............................................. 1 3.1 DOCUMENTATION APPROACH ........................................ 1 3.2 MATHEMATICAL BACKGROUND AND DATA ANALYSIS THEORY ............. 2 3.2.1 Overview .................................................... 2 3.2.2 Types of Data and Assumptions ................................... 2 3.2.3 Data Segmenting .............................................. 3 3.2.4 Mean and Trend Removal ....................................... 4 3.2.5 Spectral Leakage Reduction ..................................... 4 3.2.6 Covariance Calculations ........................................ 5 3.2.7 Fourier Transforms ............................................ 6 3.2.8 Spectra and Cross-Spectra
    [Show full text]