This outline summarizes major points covered in lecture. It is not intended to replace your own lecture notes.
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
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
Compression – Increase in density of air molecules
Rarefaction – Decrease in density of air molecules
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
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 = Fd; where F = force applied to body (N) and d = distance moved by body (m)
Units of Energy = joules (J); 1 joule = 1 Nm
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·
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(2πt + 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
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 = ma
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 )
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.
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 = ma
Law 3: for every action or force (F), there is an equal and opposite reaction or force (-F).
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 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
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