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Chapter 14: Vibrations & Waves

Chapter 14: Vibrations & Waves. Barry Latham Physics: Principles & Problems Glencoe Science, 2005. 14.1: Periodic Motion. Periodic motion - repeating motion in a regular cycle Simple harmonic motion - the restoring force is proportional to the displacement from the equilibrium position

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Chapter 14: Vibrations & Waves

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  1. Chapter 14: Vibrations & Waves Barry Latham Physics: Principles & Problems Glencoe Science, 2005

  2. 14.1: Periodic Motion • Periodic motion- repeating motion in a regular cycle • Simple harmonic motion- the restoring force is proportional to the displacement from the equilibrium position • Period (T, s)- time needed to complete one full cycle • Amplitude- maximum displacement from the equilibrium position • Physics PhysletsI.16.1 (PhET Pendulum 2.02)

  3. The Mass on a Spring • The force on a hanging spring at rest is equal to mg • More mass  more Force  more displacement • Hooke’s Law Fsp=-kx • The force exerted on a spring is equal to the spring constant (k) times the distance (x in m) the spring is moved from equilibrium • k represents the stiffness of the spring (N/m) • The negative sign refers to the Force being restorative

  4. Potential Energy in a Spring • F=-kx • When we graph F vs x, we see that the slope equals N/m (spring constant!) • Area of the graph equals Nm (Joules!) • When a spring is stretched or compressed, it is storing energy! • PEsp=(½)kx2 • When Fg=Fsp, then the spring has achieved equilibrium • Physics Physlets I.16.3, E.16.2 (PhET Pendulum 2.02)

  5. Pendulums • Pendulum- a massive object (bob) suspended by a string or rod of length, L • Fgnet= m•g•sin • FT=force of tension along the string or rod (m•g•cos) • Fg=force of gravity, always pointing down

  6. Period of Pendulum • T=2p√(L/g) • T=period (s) • L=length of pendulum support (m) • g=acceleration due to gravity (m/s2) • No mention of what the bob’s mass is!

  7. Resonance • Resonance- when small forces are applied at regular intervals to increase the amplitude of vibration • Pushing someone on a swing to make them go higher • Jumping several times on a diving board before diving • Tacoma Narrows Collapse • http://www.youtube.com/watch?v=j-zczJXSxnw&feature=fvw • Physics Physlets E16.7 (PhET Wave on a String 2.01)

  8. 14.2 Wave Properties • Mechanical Waves • Wave- a disturbance that carries matter or energy through space • Periodic wave- has a regular period • Wave pulse- a single bump or disturbance

  9. Transverse Wave • Transverse waves- motion of the medium moves perpendicularly to the direction the energy travels • Ropes, surface water waves, stringed instruments • Electromagnetic waves • Physics Physlets I.17.1 (Animation 1 & 2)

  10. Longitudinal Waves • Longitudinal waves- motion of the medium moves parallel to the direction the energy travels • Slinky pulled back • Physics Physets I.17.1 (Animation 3)

  11. Measuring a Wave • Wavelength (l, m)- distance from one point on a wave to the same point repeating • Crest- high point on a wave • Trough- low point on a wave • Frequency (f, Hertz=1/s)- the number of peaks that pass per second • Period (T, s)- the amount of time that passes from one peak to occur until the next peak occurs • T=1/f

  12. Wave Speed • Speed (m/s)- v=l/T • Phase (q)- the displacement of one wave’s peak from another’s peak • 100% In phase- peaks match up • 100% out of phase- peak matches up to trough • Amplitude- height from equilibrium to peak

  13. 14.3 Wave Behavior • Waves at Boundaries • Boundary- a change in medium • Air to water, stiff spring to soft spring, etc. • Incident wave- wave that strikes the boundary • Reflected wave- the returning wave • All of the wave is not reflected, some passes through to second medium

  14. Interference • Principle of Superposition of waves • Book definition: The displacement of a medium caused by two or more waves is the algebraic sum of the displacement caused by the individual waves • Easy Definition: Add the waves’ amplitudes to get a new wave • Physics Physlet I.17.3

  15. Wave Interference • Node- the point at which a wave doesn’t move at all • Mid-point of trough and crest • Antinode- the point at which the wave moves the most • Highest part of crest or trough • Standing wave- a wave that perfectly fits the length of the object • Always in odd multiples of ½l (l=one full wavelength) • (Sound, primarily)

  16. Waves in 2D • Wave front- a line that represents the crest of a wave • Can be circular or straight • Ray- represents the direction of travel and is perpendicular to the wave front • Angles are measured from the Normal to the reflection surface • Law of Reflection- the angle of incidence equals the angle of reflection

  17. Refraction • Law of Refraction- when changing mediums, a wave is bent (changes direction) instead of reflected • Physics Physlets I.34.1

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