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CHAPTER 2 SINUSOIDS: THE BASIC SOUND Hearing Science-- what is it? • The study of the normal process of hearing. Acoustics--the nature of sound Anatomy & Physiology of the Ear Psychoacoustics Defining 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 force Quantities Come in 2 Flavors: • Scalar Quantities – magnitude only • Vectorial or Vector Quantities – magnitude AND direction Scalar Quantities • Have magnitude only • Examples include Mass, Length, Volume • Can be added or subtracted directly Vector Quantities • Have BOTH magnitude and direction • Example: Velocity • Combining Vectors is more complicated Basic Units • • • • Length Time Mass (Charge) Other Units may be derived: • • • • Area = Length x Length (or L2) Volume = L3 Speed = Length/Time Acceleration = L/T2 Force: 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/s2 Force and Elasticity • Hooke’s Law: • Force = (-)spring constant times displacement • Stress = force per unit area (aka pressure) • Strain = change in length • Stress = Elasticity x Strain Friction • 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 DAMPING Energy & Related Concepts • WORK • POTENTIAL AND KINETIC ENERGY • POWER WORK • 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 cm ENERGY 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/sec SIMPLE 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 FRICTION SHM 4 • • • • Amplitude --Displacement Period-- Time taken to complete one cycle Frequency--Number of Cycles per Second Phase--Describing points in the Cycle A Waveform Shows Amplitude as a Function of Time DISPLACEMENT 1 PEAK PEAK-TO-PEAK 0.5 0 -0.5 -1 -1.5 TIME Period and Frequency • Frequency = 1/Period (in seconds) • Units of Frequency = cycles per second or HERTZ PHASE--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 maximum Phase Values Through a Cycle Displacement 90 1.5 1 0.5 0 -0.5 -1 -1.5 1/1/00 180 2/1/00 270 360 3/1/00 Time 4/1/00 AMPLITUDE 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 Amplitudes FREE 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 Stiffness FORCED VIBRATION • Force is applied back and forth • Vibration occurs at the frequency of the applied force • Object’s mass and stiffness determine amplitude of vibration