Physics Notes Ch 11

11 - 1 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=2m/k

11-4 The Simple Pendulum

• Period of oscillation does not depend on amplitude

• Force diagram - Fig 11-12 pg. 319

• Pendulum motion does not depend on the mass, ONLY length of string.

• Period of a pendulum T=2L/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

11 - 7 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 11-23

• 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 11-24 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