3 Periodic Motion Any repetitive, or cyclical, types of motion Examples?Simple Harmonic Motion is a specialized form of periodic motion
4 Simple Harmonic Motion Periodic vibration around an equilibrium positionRestoring force must beproportional to displacement from equilibriumin the direction of equilibrium
5 Restoring ForceThe push or pull that brings the mass back towards equilibriumThe restoring force of a pendulum is a component of the bob’s weight.The restoring force for a mass-spring system is from the stretch (or compression) of the spring
6 Simple Harmonic Motion Common examples include a mass-spring system or a pendulumFor a pendulum, SHM only for small angles (within 10 degrees of vertical)
7 Describe speed, acceleration, and restoring force at each point. Relaxed LengthDescribe speed, acceleration, and restoring force at each point.
8 Describe speed, acceleration, and restoring force at each point.
20 Some general terminology… Pulse – a single disturbance, single cyclePeriodic wave – continuous, repeated disturbancesSine wave – a wave whose source vibrates with simple harmonic motionMedium – whatever thewave is traveling through
21 Wave MotionA wave is the motion of energy away from a source of periodic disturbance.Mechanical waves require a physical medium to travel through.Examples: sound, disturbance in a slinkyExamples of physical media are water, air, string, slinky.
22 Electromagnetic waves Do not require a physical medium.Examples include x-rays, visible light, radio waves, etc.
23 Transverse WavesParticles of the medium move perpendicular to the direction of energy transferYou should be able to identify crests, troughs, wavelength (distance traveled during one full cycle), and amplitudeCrestTrough
24 Longitudinal WavesParticles of the medium move parallel to the direction of energy transfer (slinky demo)Be able to Identify compressions, rarefactions, wavelengthsCompressions Rarefactions
25 Waves transfer energyNote that, while energy is transferred from point A to point B, the particles in the medium do not move from A to B.Individual particles of the medium merely vibrate back and forth in simple harmonic motionThe rate of energy transfer is proportional to the square of the amplitudeWhen amplitude is doubled, the energy carried increases by a factor of 4.
26 Wave speedWave speed is determined completely by the characteristics of the mediumFor an unchanging medium, wave speed is constantCalculate speed of a wave by multiplying wavelength by frequency.v = f x λ
27 Practice #1Q: Microwaves travel at the speed of light, 3.00108 m/s. When the frequency of microwaves is 9.00 109 Hz, what is their wavelength?A: m
28 Practice #2Q: The piano string tuned to middle C vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound waves produced by the string.A: 1.30 m
31 InterferenceThe combination of two or more waves in a medium at the same time.Matter cannot occupy the same space at the same time, but energy can.The Superposition Principle describes what happens when waves interfere…Waves (energy) pass through each other completely unaffectedThe medium will be displaced an amount equal to the vector sum of what the waves would have done individually
34 Constructive Interference Waves are on the same side of equilibrium.Waves meet, combine according to the superposition principle, and pass through unchanged.Amplitude larger than originals
35 Destructive Interference Waves are on the opposite sides of equilibrium.Waves meet, combine according to the superposition principle, and pass through unchanged.Amplitude smaller than at least one original wave