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PSYCH 3A03 (56)
Paul Faure (56)

Week1 outline

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McMaster University
Paul Faure

This outline summarizes major points covered in lecture. It is not intended to replace your own lecture notes. Lecture 01 Sound Requires Vibration  Any object that can vibrate can transmit or receive sound  Any object with mass and elasticity can vibrate, and any object with mass has elasticity  Sound can travel through anything that vibrates, not just air Lecture 02 Air Pressure  Air pressure is the weight of air surrounding an object  Air pressure provides a force on the eardrum  Ear is very sensitive, can detect pressure changes much smaller than the static air pressure  Static air pressure is not audible  Due to gravity, air particles are more compressed and have a higher density closer to earth’s surface Properties of the Sound Source  Input force is required to set an object into vibration  Amplitude of vibratory displacement  input force (Hooke’s Law) Sound and Vibrations  Systematic vibrations of an object are transmitted to the surrounding air molecules (mass of air)  Systematic vibrations of an object will cause local changes in air pressure and thus the density of air molecules  Compression – Increase in density of air molecules  Rarefaction – Decrease in density of air molecules Waves  For sound waves there are two types of disturbances to consider 1. Rate of particle vibration (frequency of vibration) 2. Rate of wave propagation (speed of sound in medium)  Discussed two major types of wave motion 1. Transverse waves: direction of particle oscillation is perpendicular to direction of wave propagation 2. Longitudinal waves: direction of particle oscillation is parallel to direction of wave propagation  Sound is a longitudinal wave Energy  Measure of the capacity to do work  Conservation of energy: energy can be converted from one form to another but not created/destroyed  Work — a transfer of energy; a force is applied to a body causing it to move in the direction of the force  Work = Fd; where F = force applied to body (N) and d = distance moved by body (m)  Units of Energy = joules (J); 1 joule = 1 Nm  Potential energy (PE) versus kinetic energy (KE)  Potential Energy (PE) = stored energy  Kinetic Energy (KE) = energy of work  PE + KE = 0 (Law of Conservation of Energy)  Pendular motion: energy transfer between PE and KE; an example of simple harmonic motion  Simple harmonic motion = uniform circular motion  Friction provides a limit on oscillatory motion (sound energy does not travel forever)  Equation: Angular rotation frequency is ω = 2π· Pendular motion  At point of zero displacement point (bottom), KE is maximum  At point of maximum displacement point (top; either side), PE is maximum Psych 3A03 14 September 2012 Week 0+1 Dr. Paul A. Faure  Inertia causes pendulum to swing past equilibrium point  Pendular momentum = mass x velocity (kg·m·s ) -1  Total energy = PE + KE (Conservation of energy)  Friction opposes motion and causes KE to transfer to thermal energy in medium (this is why sound does not propagate forever) Simple Harmonic Motion  Simple harmonic motion can be defined as projected uniform circular motion  Uniform circular motion occurs when a body moves around the circumference of a circle at a constant rate in degrees per second (˚/s)  For any object executing uniform circular motion, we expect the angle () to increase linearly with time.  = t , where  = angular rotation frequency ( = 2πƒ ; ƒ = frequency or rate of rotation) and t = time. Time domain waveform  Time domain: amplitude of displacement as a function of time  Equation: D(t) = ·sin(2πt + θ) or D(t) = ·sin(t + θ), where:  A = peak amplitude,  = 2πƒ , t = time and θ = starting phase (or position)  Sinusoidal motion: an example of simple harmonic (uniform circular) motion Tutorial 01 Fundamental Physical Quantities  Length: distance or spatial separation  Mass: quantity of physical matter (independent of weight which is a measure of gravity on mass!)  Time: difficult to define; can use tools such as an atomic clock to define basic units of time  Temperature: the average energy of atoms in a system  All other physical quantities can be derived from these fundamental quantities. Derived Physical Quantities  Displacement (x): a change in position, specified by calculating the distance from a reference position to an ending position, and by noting the direction of movement  Velocity (c): displacement per unit time  Acceleration (a): change in velocity per unit time  Force (F): the product of mass and acceleration, F = ma  Pressure (P): the amount of force per unit area, P = F/A Scalar versus Vector  A scalar value is a measurement without direction. Example: I am 1.8m tall.  A vector value is a measurement with direction. Example: I live 5km North West from campus.  Simple addition and subtraction can be done with scalar but NOT vector quantities Mass (m), Density () & Pressure (P)  Mass (m) = Amount of matter present (kg, lbs)  Density () = mass per unit volume (kg/m , lb/in ) 2  Pressure (P) = force per unit area (N/m = Pa)  Force of gravity causes air pressure (and density) to increase toward the Earth’s surface.  Air molecules are more “compressed” at sea level than at higher levels in the atmosphere.  The “static” atmosphere pressure is not audible; however, systematic oscillations in the surrounding air pressure may be audible. Lecture 03 Elasticity  Elasticity is the tendency to resist and recover from distortion.  Elasticity is the restoring force that allows an object to recover from a distorting force.  Air elasticity and recovery is molecule movement that accounts for sound. Psych 3A03 14 September 2012 Week 0+1 Dr. Paul A. Faure  An input force is needed for object vibration and to produce a sound.  Newton’s Laws of motion (see below)  Hooke’s Law: displacement amplitude is proportional to the applied (input) force.  Mass and elasticity are fundamental concepts for understanding sound and vibration.  Compression – increase in density of air molecules relative to static (ambient) pressure.  Rarefaction – decrease in density of air molecules relative to static (ambient) pressure. Newton’s Laws of Motion  Law 1: an object in a state of uniform motion tends to remain in a state of uniform motion unless an external force is applied to it.  Law 2: relationship between mass of object (m), its acceleration (a) and the applied force (F) is: F = ma  Law 3: for every action or force (F), there is an equal and opposite reaction or force (-F). Unit circle  cosθ describes x-axis projected motion  sinθ describes y-axis projected motion  If you understand the relationship of sinθ and cosθ you can understand properties of sine waves.  sinθ and cosθ are constant and do not vary with radius (amplitude) of unit circle (pure tone) Sound transmission  Sound must travel through a medium.  There is no sound in a vacuum (e.g. space).  Amplitude of displacement is change in excursion of air molecules  Particle displacement and particle velocity are similar to the relationship between cosθ and sinθ functions (i.e. 90 out of phase) Sound Amplitude (A)  Amplitude (A) of air particle displacement is proportional to applied force  Magnitude of restoring force of elasticity is directly  to magnitude of input force of displacement (Hooke’s Law)  Amplitude is a vector quantity; it has both a magnitude and a direction.  Amplitude of a sound vibration is independent of the frequency of vibration. Displacement (x), velocity (v), acceleration (a), pressure (Pa)  Sound may be produced when air particles are set into vibration.  Air particle displacement causes changes in the density of air molecules.  Pressure is force per unit of area, hence air pressure also changes.  Relationship between displacement (x), velocity (v), acc
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