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# Midterm Study Guide CD 411

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This 6 page Study Guide was uploaded by Kara Mockaitis on Tuesday March 10, 2015. The Study Guide belongs to CD 411 at University of Alabama - Tuscaloosa taught by Dr. Buhr in Spring2015. Since its upload, it has received 48 views.

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Date Created: 03/10/15

Midterm Chapter 1The Nature of Sound Waves A source of sound must be able to vibrate with two properties 0 Mass m the amount of matter present 0 Applies to gases liquids amp solids 0 Weight is an attractive gravitational force mass is the quantity of matter present 0 Density p the mass per unit volume p m v A quantity derived from another quantity mass Unit of measure kgm3 o Elasticity E property that enables recovery from distortion of shape or volume 0 Density is restored for air 0 Elastic limit when enough force is applied matter will either break or become permanently distorted 0 Unit of measure Nmquot2 A medium must be capable of being set into vibration to transmit sound The property addressed by Newton39s rst law is called inertia o Newton39s Inertial Law all bodies remain at rest or in a state of uniform motion unless another force acts in opposition o Magnitude of inertia is directly proportional to the mass thus mass is a measure of inertia 0 Ex tuning fork Newton39s Third Law with every force there must be an equal and opposite reaction force 0 Ex hammer amp nail bat amp ball 0 Force cannot exist alone 0 Vibration elasticity is the reaction force to inertia 0 Density increases with compression 0 Density decreases with rarefaction Sound characterized by propagation of density changes through elastic medium Fundamental Physical Quantities Length a measure of distance the amount of spatial separation between two points 0 Unit of measure m 0 Mass the quantity of matter present 0 Unit of measure kg 0 Time a quantity expressed in seconds minutes hours etc 0 Unit of measure 5 A derived quantity is a quotient or product of fundamental or of fundamental and derived physical quantities 0 Displacement x a change in position vector 0 Velocity c the amount of displacement per unit time or the timerate of displacement c x t vector 0 Speed scalar s d t 0 Unit of measure ms Acceleration a the timerate change in velocity a c2 c1 t vector and derivative of velocity 0 Unit of measure msquot2 0 Ex a care moves around a circular tract at a constant speed Is it accelerating Yes direction is changing hence velocity is changing Velocity cannot change without acceleration 0 Force F a push or pull or that which imparts acceleration to a mass distortion of matter andor acceleration of matter F ma 0 Newton39s 2nd Law object has mass inertia which opposes change in motion a force is applied to overcome inertia a F m 0 Unit of measure N 0 Pressure p force per unit area p F A 0 Unit of measure Nmquot2 or Pa Hooke39s Law Magnitude of restoring force is directly proportional to magnitude of displacement Fr kx o Stiffness k the spring constant 0 Compliance the inverse of stiffness stiffer springs are less compliant Simple Harmonic or Sinusoidal Motion 0 Gravity restoring force in a pendulum Force due to inertia Fi in a pendulum maximal at equilibrium and zero at maximum displacement where motion is momentarily halted o Restoring force Fr in a pendulum maximal at maximum displacement and zero at equilibrium Momentum the product of mass and velocity M mc 0 Both are maximal at equilibrium and zero at maximum displacement where motion is momentarily halted Energy the capacity to do work change in matter 0 Work W product of the force applied and the distance moved W Fd 0 Unit of measure Nm orjoule Potential energy PE stored energy PE wgh wweight ggravity hheight o Maximal at maximum displacement and zero at equilibrium 0 Kinetic energy KE energy of motion KE 12 mcquot2 o Maximal at equilibrium where c is maximal and zero at maximum displacement where motion is momentarily halted and c0 o Frictional resistance a force that opposes motion and thus limits velocity 0 Frequency f the rate of vibratory motion and the number of quotcycles per second cpsquot f 1 T 0 Unit of measure hertz Hz 1 Hz1cps 0 Cycle movement from equilibrium to maximum displacement in one direction back to equilibrium on to maximum displacement in the opposite direction then back to equilibrium 0 Period T the time required to complete one cycle T 1 f 0 Unit of measure seconds per cycle 0 Period of a pendulum T 2m LG I T 0lt L T 0 1 G lnrelationtoffoc1L femG Source frequency of vibration characteristics air particles 0 Medium speed of wave propagation properties 0 s E 9 Two types of wave motion 0 Transverse vibration of medium is 90 degrees re direction of wave propagation 0 Longitudinal direction of particle movement is parallel to direction of wave movement Chapter 2Simple Harmonic Motion Waveform o Timedomain waveform a plot of change in amplitude of displacement x over time SHM projected uniform circular motion Springmass system motion rectilinear straightline not circular Triangle o The ratio xr is a constant for any given angle 0 The sine of the angle corresponds to percentage of maximum displacement Xmax Five dimensions of sine waves 0 Amplitude 0 Particle velocity leads particle displacement by 90 degrees 0 Particles acceleration leads particle displacement by 180 degrees 0 rms standard deviation of all instantaneous amplitudes rms 0707A 0 Mean square rmsquot2 or Aquot22 o Fullwave recti ed average FWavg arithmetic mean of all instantaneous amplitudes in the recti ed wave FWavg 0636A o Halfwave recti ed average HWavg0318A 0 Frequency rate in Hz at which a sinusoid repeats itself number of cycles per sec expressed in hertz Hz 0 Hz to kHz divide by 1000 0 Natural frequency for all vibratory systems fnat k m fnatocxk fnatoc1xm 0 Natural frequency of string f 1 2L t m fnatoc12L fnatocxtfnatocllxm o 1 radian573 degrees 0 Angular velocity on 2nf 2n radians s 0 Period time required to complete one cycle number of seconds per cycle expressed in sec 5 o s to ms multiply by 1000 0 Phase 0 Starting phase angle in degrees at moment rotation begins 0 Instantaneous phase angle of rotation at some speci ed moment in time Wavelength A distance traveled during one period A S f 0 Friction limits velocity 0 Elasticity is in phase with displacement o Momentum and damping are in phase with velocity 0 Damping factor df ratio of amplitudes of any two consecutive cycles is a constant df In AlA2 Lowdamped system decays slowly Highdamped system decays rapidly Critical damping system oscillations almost stop immediately 0 Impedance Z components Resistance R energy is dissipated KE to TE 0 Measured in ohms and frequency independent Reactance X energy is stored as PE KE to PE 0 Mass reactance Xm Compliant reactance Xc Chapter 3Logarithms and Antilogarithms Scales Nominal objects are the same or different categorical Ordinal two things are the same or different and one object is the same as another or it has more or less of some quantity than another Interval size of interval between adjacent numbers is known and is a constant 0 Size of interval is called the base Ratio one unit on scale is so many times greater or less than another 0 Also known as exponential scae xquotn o XAO1 o Xquot1X o Xquotn1xquotn Exponential Laws Law 1 xquotaxquotbxquotab Law 2 xquotaxquotbxquotab Law 3 xquotaquotbxquotab Log Laws Law 1 Law 2 Log abLog a Log b Log abLog a Log b Law 3 Log aquotbb Log a Law 4 Log 1a Log a Log 10 Log 23 Log 348 Log 460 Log 570 Log 678 Log 785 Log 890 Log 996 Log 101 Chapter 4Sound Intensity and Sound Pressure The Decibel Sound energy Power the rate at which energy is transferred per unit time o Expressed in wattsjoues Energy the capacity to do work Absolute power one sound wave is compared with the absolute power in another reference wave 0 LevelWxWr Wx power of interest and Wr reference power Intensity energy per second per square meter wattmquot2 o Levelxlr N belsog 10 IxIr bes mean lxgtlr and bes mean lxltlr 10 fold change10 dB change 2 fold change 3 dB change Reference intensity must always be speci ed dB lL lr10quot12 wattmquot2 Pressure force per unit areaNmquot2 or 1 Pa 0 dB20 log 10 PXPr 0 dB SPL Pr2 x 10quot1 uPa OOOOO o 2 fold change6 dB change 0 10 fold change 20 dB change 0 Intensity is proportional to pressure squared

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