CHAPTER 2Hearing Science-- what is it?Defining SOUNDVIBRATIONElasticity is:Quantities Come in 2 Flavors:Scalar QuantitiesVector QuantitiesBasic UnitsOther Units may be derived:Force: A push or a pullForce and ElasticityFrictionFriction produces ResistanceEnergy & Related ConceptsWORKENERGY COMES IN 2 FLAVORSPOWERSIMPLE HARMONIC MOTIONSimple Harmonic Motion 2SHM 3SHM 4A Waveform Shows Amplitude as a Function of TimePeriod and FrequencyPHASE--Each cycle broken up into 360 degreesPhase Values Through a CycleAMPLITUDE MEASURESFREE VIBRATIONFORCED VIBRATIONCHAPTER 2SINUSOIDS: THE BASIC SOUNDHearing Science-- what is it?•The study of the normal process of hearing.Acoustics--the nature of soundAnatomy & Physiology of the EarPsychoacousticsDefining SOUND•Psychological definition: Sound is a stimulus with the capability of producing an audible sensation.•Physical definition: Energy produced by an object in vibration and transmitted through a medium.VIBRATION•vibration is the movement of an object from one point in space to another, and usually back to the first point. •Objects that can be set into vibration have two properties: –elasticity –inertia (fundamental feature of mass)Elasticity is:•The property that allows an object or substance to return to its initial shape or state when it is deformed, distorted or displaced.Tuning fork: stiffness provides restoring forceSwing: gravity provides restoring forceQuantities Come in 2 Flavors:•Scalar Quantities–magnitude only•Vectorial or Vector Quantities–magnitude AND directionScalar Quantities •Have magnitude only•Examples include Mass, Length, Volume•Can be added or subtracted directlyVector Quantities•Have BOTH magnitude and direction•Example: Velocity•Combining Vectors is more complicatedBasic Units•Length•Time•Mass•(Charge)Other Units may be derived:•Area = Length x Length (or L2)•Volume = L3•Speed = Length/Time•Acceleration = L/T2Force: A push or a pull•Force = Acceleration x mass•Therefore Force = ML/T2•MKS force unit is Newton = 1 kg m/s2•cgs unit is dyne = 1 g cm/s2Force and Elasticity•Hooke’s Law:•Force = (-)spring constant times displacement•Stress = force per unit area (aka pressure)•Strain = change in length •Stress = Elasticity x StrainFriction•Energy converted into heat when molecules rub against each other.•To move an object, the applied force must overcome friction.•Effect of Friction is “Resistance”Friction produces Resistance•Resistance = ratio of Force to resulting velocity (R = f/v)•measured in Ohms •Acoustically, we talk about the influence of friction as DAMPINGEnergy & Related Concepts•WORK•POTENTIAL AND KINETIC ENERGY•POWERWORK•Force applied through a distance•No motion--no work•Work = force x distance = ML/T2 x L •Units JOULE = 1 Newton Meter • erg = 1 dyne cmENERGY COMES IN 2 FLAVORS•Kinetic-- Energy of motion• (Inertia can be thought of as the ability to store kinetic energy)•Potential--Energy of position• (Elasticity --ability to store potential energy)POWER•Rate at which work is done•Work/Time•Unit Watt = joule/second or 107 erg/secSIMPLE HARMONIC MOTION•Vibration involves interplay of force, inertia, elasticity, and friction•Applying a force displaces object •Overcoming inertia•Traveling away from rest until ?Simple Harmonic Motion 2•Why does object stop and then move back toward rest?•Why doesn’t the object then stop at rest?•Where is potential energy the greatest?•Where is kinetic energy the greatest?SHM 3•Why does displacement decrease over time?•RESISTANCE•-- Energy is lost to HEAT through FRICTIONSHM 4•Amplitude --Displacement•Period-- Time taken to complete one cycle•Frequency--Number of Cycles per Second•Phase--Describing points in the Cycle-1.5-1-0.500.51TIMEDISPLACEMENTA Waveform Shows Amplitude as a Function of TimePEAKPEAK-TO-PEAKPeriod and Frequency•Frequency = 1/Period (in seconds)•Units of Frequency = cycles per second or HERTZPHASE--Each cycle broken up into 360 degrees•0 degrees = 0 displacement and about to head positively•90 degrees = positive maximum•180 degrees=0 disp. About to head negatively•270 degrees= negative maximumPhase Values Through a Cycle-1.5-1-0.500.511.51/1/00 2/1/00 3/1/00 4/1/00TimeDisplacement90180270360AMPLITUDE MEASURES•Instantaneous- amplitude at any given instant•Peak•Peak to Peak•Root Mean Square--A way of getting average amplitude•=Square root of Averaged Squared AmplitudesFREE VIBRATION•Pendulum illustration represents FREE VIBRATION•Force applied and object allowed to respond•Frequency of Free Vibration =Resonant or Natural Freq.•--determined by the object’s Mass and StiffnessFORCED VIBRATION•Force is applied back and forth•Vibration occurs at the frequency of the applied force•Object’s mass and stiffness determine amplitude of