Physics Notes Ch 11

1. Physics Notes Ch 11

2. 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

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

4. 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

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

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

7. 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=2L/g • Clocks – Must supply energy to the pendulum to maintain its swing - Falling weights

8. 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

9. 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

10. 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.

11. Rope waves • pg. 325 Fig 11-23 • Crest – Peak of wave motion • Trough – Valley of wave motion

12. 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

13. 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

14. 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)

15. 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

16. 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

17. 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.

18. 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.

19. 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