DOCSLIB.ORG

Ch 14 Lecture Hand

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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. Definitions Compression – high molecular density and high air pressure Rarefaction – low density and Similarly, the antinode of a low pressure standing wave acts like a mass- spring system in SHM. Waves Definitions Audible – longitudinal waves TRANSVERSE LONGITUDINAL that lie within the range of sensitivity of the human ear, The vibrations of the elements The motion of the elements of approximately 20 to 20,000 Hz of the medium are at right the medium is back and forth angles to the direction of travel along the direction in which the Infrasonic – frequencies below of the wave. wave travels the audible range Ultrasonic – frequencies above the audible range Equations Concept Wave Speed on a String As seen in the previous equation, the tension in the string and v = √(T/μ) type of string is what decides the speed of the wave. Where v is wave speed, T is tension, and μ is mass of string per This is a common theme for waves. The medium that the wave unit length called linear density (mass/length) travels through is what decided the speed, NOT the frequency or amplitude. Linear Density μ = m/L For waves on a string, another way of talking about the medium is the tension in the string and the linear mass density of the string. Where μ is linear density, m is mass of rope, and L is length of rope If the medium is constant, the speed is constant. SI Unit: kg/m Equation Intensity of a Wave Definitions I = P/A Wave fronts – circular arcs that represents lines of maximum intensity Where I is intensity, P is power, and A is area Rays – radial lines pointing outward from the source and perpendicular to wave fronts SI Unit: Watts per Plane waves – wave fronts so meter squared far from the source they are (W/m2) approximately parallel planes Definitions Superposition principle – two waves combine to form the The Doppler Effect resultant wave Standing wave – wave that appears to stand still but is really The wavelength shortens and the frequency increases (sounds two waves interfering seem higher pitch) when an observer is moving toward the sound source. Node – location of zero net displacement due to destructive interference Antinode – largest amplitude of standing wave due to Or constructive interference Fundamental frequency – lowest possible frequency The wavelength increases and the frequency decreases (sounds First harmonic – another name for fundamental frequency seem lower pitch) when an observer is moving away from the Second harmonic – also called first overtone, is twice the first sound source. harmonic Third harmonic – also called second overtone, is three times the first harmonic Equations Harmonic Series for Standing Waves on a String and Pipe Open at Both Ends fn = nv/2L Where f is the frequency, n is the harmonic number, v is the speed of the waven on the string, and L is the length of the string. Where fn is the frequency, n is the harmonic number, v is the speed of the wave in air, and L is the length of the pipe Harmonic Series for Standing Waves in Pipe Open at One End fn = nv/4L Where fn is the frequency, n is the harmonic number, v is the speed of the wave in air, and L is the length of the pipe. Note: only odd harmonics are allowed Definitions Forced vibration – an object is periodically pushed Resonant frequency – natural frequency of the system Resonance – the forced vibration matches the resonant frequency and the amplitude increases timbre – characteristic sound quality Resonance Definition If a loud sound is heard for the first harmonic, the length Beats – alternating loudness of air is approximately ¼ of a full wave so you can take L due to two waves of slightly and multiply by four to get an estimate of the different frequencies wavelength. interfering The number of beats per It is better to find two consecutive loud spots and second you hear is how far off subtract them to find the length of a football (half of a the two frequencies are from wave) and then double that to get full wavelength. each other in Hz..
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 mpt6@cox.net 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]
  • 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]
  • 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
    [Show full text]