Hooke's Law
-the restoring force is directly proportional to the displacement of the mass
Hooke's Law Equation
spring force = -(spring constant x displacement)
Spring Constant
-the stiffness of the spring
-SI Units N/m
Simple Harmonic Motion
-vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium
Simple Harmonic Motion at Max Displacement
Restoring force in x direction is at max
Acceleration is at max
Velocity is at zero
Simple Harmonic Motion at Equilibrium
Restoring force in x direction is zero
Acceleration is zero
Velocity is at max
Amplitude
-the max displacement from equilibrium
Period
-the time that it takes to a complete cycle to occur
Frequency
-the number of cycles or vibrations per unit of time
Relationship of Frequency and Period
Period = 1/frequency
Frequency = 1/period
Period of a Simple Pendulum in Simple Harmonic Motion
period = 2(pie) x square root of (length divided by free-fall acceleration)
Period of a Mass-Spring System in Simple Harmonic Motion
period = 2(pie) x square root of (mass divided by spring constant)
Medium
-a physical environment through which a disturbance can travel
Mechanical Wave
-a wave that requires a medium through which to travel
Electromagnetic Wave
- a wave that can travel through a vacuum
Sine Wave
-a wave whose source vibrates with simple harmonic motion
Transverse Wave
-a wave whose particles vibrate perpendicularly to the direction of the wave is traveling
-the y axis is displacement
Waveform
-can represent either the displacements of each point of the wave at a single moment in time or the displacements of a single particle as time passes
Crest
-the highest point above the equilibrium position
Trough
-the lowest point below the equilibrium position
Wavelength
-the distance between two adjacent similar points of a wave such as from crest to crest or from trough to trough
Longitudinal Wave
-a wave whose particles vibrate parallel to the direction the wave is traveling
-the y axis is density or pressure
-has compressed and stretched regions, compressed being the crest and stretched being the trough
Speed of a Wave
speed of a wave = frequency x wavelength
Waves
-transfer energy
Superposition Principle
-method of summing the displacements of waves
Constructive Interference
-a superposition of two or more waves in which the individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Destructive Interference
-a superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Complete Destructive Interference
-at the instance when two waves overlap, they completely cancel each other out
Compression
-particles move closer together
Rarefraction
-particles are spread farther apart
Interference of Compression and Rarefraction
-the interference is destructive
Free Boundary
-waves are reflected and remain on the same side
Fixed Boundary
-waves are reflected and inverted
Standing Wave
-a wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere
-only certain frequencies produce standing waves (2L, L, 2/3L)
Node
-a point in a standing wave that maintains zero displacement
Antinode
-a point in a standing wave, halfway between two nodes, at which the largest displacement occurs