Simple Harmonic Motion.docx

September 10 , 2013 Psych 3A03: Audition Simple Harmonic Motion Whay is Air Pressure - Atoms and molecules make up layers in the atmosphere. Despite their size, they exert some weight on us. We feel this weight as pressure - Air pressure is the weight of air surrounding an object - The weight of air is directly related to the number of air molecules - Air pressure depends on the number of molecules in a given area (space) and how fast these molecules are moving - Density decreases with altitude due to gravity - Net movement is approximately 0 unless there is force Properties of the Transmitting Medium - Air molecules  400 billion molecules per in 3or 1.21kger m 3  Molecules are moving randomly at about 1500km/hr due to thermal (Brownian) motion  More or less evenly distributed and moving equally in all directions (average molecular velocity = 0m/s)  Air molecules exert a force (atmospheric pressure) on other objects (e.g. tympanic membrane or ear drum)  Standard atmospheric pressure = 101,325 Pa  Air velocity threshold of hearing = 5x10 m/s-8  Thus, any systematic (repeatable) oscillations in air pressure (velocity) may be audible Mass (m), Density (p), and Pressure (P) - Mass (m) = amount of matter present (kg, lbs) - Density = mass per unit volume (kg/m ;lb/in ) 3 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 - Sea level = 14.7lb/in or 101,325 Pascals - @10 miles = 1.57lb/in ; @25 miles = 0.039lb/in 2 - This static atmospheric pressure is not audible - However, systematic oscillations in the surrounding air pressure may be audible Elasticity (E) - All matter becomes distorted (in shape or volume) when a force is applied to it - Elasticity is the tendency to resist and recover from distortion (e.g. tuning fork, mass attached to a spring) - The distortion of air molecules results in their compression (i.e. increase in density) - Tendency of air molecules to return to former volume (density) after compression is a restoring force - Restoring force = elasticity = ability to recover from a distortion force - All matter is elastic, but different objects differ in their elasticity Properties of the Sound Source - Again, the only prerequisite for producing sound is that an object must vibrate - For an object to vibrate it must posses a mass and elasticity (all molecular objects have both) - Amplitude of vibratory displacement is proportional to the input force Vibrations From a Tuning Fork - Stretching the tuning force causes a displacement and compresses the air molecules adjacent to the tuning fork - As the restoring force of the elasticity of the tuning fork brings the tuning fork back to its resting state, return to static air pressure and the compressed molecules collide with surrounding molecules propagating the wave - Tuning fork continues to move in until the restoring force opposes the motion and slows it down, less air molecules are now present next to the tuning fork - Restoring force moves back to starting position = static air pressure - Oscillation continues causing another compression - The distance between the two compressions is one wave of oscillation (period of oscillation) Newton’s Laws of Motion 1. An object in state of uniform motion tends to remain in a state of uniform motion unless an external force is applied to it 2. The relationship between an object’s mass m, its acceleration, and the applied force F, is: F = ma 3. For every action ro force D, there is an equal and opposite reaction or F = -F Newton’s First Law of Motion: Inertia - Law #1: All bodies remain at rest or in a state of uniform motion unless another force acts in opposition  i.e. all object’s have mass and thus inertia  Mass attached to spring continues to oscillate and the tines of a tuning fork continues to vibrate back and forth past their original equilibrium  Amount of inertia proportional to the objects mass  Displacement amplitude proportional to applied force (Hooke’s’ Law)  Restoring force of elasticity returns the tines of the tuning fork toward the equilibrium point  Inertial force causes the tines to move past the equilibrium point  A force is required to move (deform) a mass attached to a spring  The mass has inertia  The spring has a stiffness (k)  Elasticity opposes the force that is required to displace the mass 