Physics Notes Ch 11

Simple Harmonic Motion Vibration/Oscillation – Movement about an equilibrium position Periodic - Repeats itself back and forth over the same motion Equilibrium Position – Position where the net force is zero on an object

Spring F = -kx Spring constant – Force required to stretch a spring a unit of length Displacement – Distance of disturbance from it’s equilibrium position

Cycle – One complete repetition of periodic motion. May start in any location. Period – Length of time it takes for a cycle to complete. It is the inverse of frequency. Amplitude – The maximum distance from the equilibrium that occurs in periodic motion. f = 1/T T = 1/f

Simple Harmonic Motion - vibrating system in which the restoring force is directly proportional to the negative of the displacement

Springs Why does spring oscillation stop? Friction converts mechanical energy into thermal energy Period and frequency not effected by amplitude T=2  m/k

11-4 The Simple Pendulum Period of oscillation does not depend on amplitude Force diagram - Fig pg. 319 Pendulum motion does not depend on the mass, ONLY length of string. Period of a pendulum T=2  L/g Clocks – Must supply energy to the pendulum to maintain its swing - Falling weights

11-6 Resonance Natural frequency - frequency of a vibrating system when it is set into motion Resonance – A large increase in the amplitude of a vibration when a force is applied at the natural frequency of the medium or object. Swing set – must pump legs at specific times during natural frequency of swing. Depends on length of swing. Push every other time at _ resonant frequency Vibrations produce sounds at natural frequency

Resonance – Good and Bad effects – Radio station tune to resonance frequency, bridges, earthquakes Tacoma Narrows Bridge - Long (2800 ft) and narrow (40 ft) bridge. Wind caused oscillations. Very flexible structure. Wind was perpendicular to bridge, causing vortices to form creating a translating (twisting) motion on the bridge deck. Close to the natural frequency of the bridge (amplified). Loma Prieta Earthquake – Bay Mud increased amplitude of vibrations causing more damage. Fire caused by broken gas lines, not water due to broken water lines. Website Demo

Waves Waves – The movement of energy from one place to another without any accompanying matter Pulse wave – dominos, spring demo Periodic wave – All pulses have the same size and shape repeats itself over a distance of one wavelength and a time of one period.

Rope waves pg. 325 Fig Crest – Peak of wave motion Trough – Valley of wave motion

Wavelength ( ) – Distance that a wave pattern repeats. Frequency (f) – Number of times a periodic motion repeats in a unit of time. Inverse of period. Amplitude (A) - Maximum height of a crest or depth of a trough relative to the equilibrium level Speed = wavelength X frequency V = f

11-8 Transverse and Longitudinal Waves Transverse wave – vibration of medium is perpendicular to the motion of the wave. Longitudinal wave – Vibration of the medium is in the same direction as the motion of the wave. Spring ( Fig pg. 326) – Vertically – Transverse Horizontally –Longitudinal

Transverse waves cannot exist in fluid Earthquake waves Three types – Surface waves, P & S waves (through interior) Earth radius 6400 km (4000 miles) Waves partially reflected through different regions and change speeds with physical conditions (elasticity and density)

Longitudinal waves – P waves (compression) caused by expansion and contraction of rocks near surface. Pass through solids, liquids and gasses. Transverse waves - S waves (Shear waves) rolling motion. Most damaging. Locate epicenter of earthquake by triangulation

11-11 Reflection and Superposition Reflection - return pulse returns inverted Superposition – The combination of two or more waves at a location in space (add together) Waves pass as if the other was not there – pebbles in a pond Interference - The superposition of two waves

In Phase - Produce crests at the same time and troughs at the same time. Same wavelength and frequency. Constructive interference - Crest meets crest, trough meets trough. Amplitude increases. Destructive interference - Crest meets trough. Amplitude decreases. Diffraction - The spreading of waves passing though a barrier. Depends on size of opening and wavelength. Overhead.

11-12 Standing Waves Standing Waves - Confined periodic wave. Appears to stand still in the horizontal direction. Standing wave - The inference pattern produced by two waves of equal amplitude and frequency traveling in opposite directions. Node - One of the positions in a standing wave where there is no movement, amplitude equals zero. Antinode - One of the positions in a standing wave where there is maximal movement, amplitude is a maximum.

Distance between adjacent nodes or adjacent antinodes is one-half wavelength Spring Demo Fundamental frequency - Lowest resonant frequency for an oscillating system. Also has longest wavelength. Harmonic - A frequency that is a whole number multiple of the fundamental frequency. Spring demo