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