Chapter 14: Vibrations & WavesBarry Latham

Physics: Principles & ProblemsGlencoe Science, 2005

14.1: Periodic MotionPeriodic 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 Physlets I.16.1 (PhET Pendulum 2.02)

The Mass on a SpringThe force on a hanging spring

at rest is equal to mgMore mass more Force more

displacement

Hooke’s Law Fsp=-kxThe 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

Potential Energy in a SpringF=-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)

PendulumsPendulum- 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

Period of PendulumT=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!

ResonanceResonance- when small forces are applied at regular

intervals to increase the amplitude of vibrationPushing someone on a swing to make them go higherJumping several times on a diving board before diving

Tacoma Narrows Collapsehttp://

www.youtube.com/watch?v=j-zczJXSxnw&feature=fvw

Physics Physlets E16.7 (PhET Wave on a String 2.01)

14.2 Wave PropertiesMechanical Waves

Wave- a disturbance that carries matter or energy through space

Periodic wave- has a regular period

Wave pulse- a single bump or disturbance

Transverse WaveTransverse waves- motion of the medium moves

perpendicularly to the direction the energy travelsRopes, surface water waves, stringed instrumentsElectromagnetic waves

Physics Physlets I.17.1 (Animation 1 & 2)

Longitudinal WavesLongitudinal waves- motion of the medium

moves parallel to the direction the energy travelsSlinky pulled back

Physics Physets I.17.1 (Animation 3)

Measuring a WaveWavelength (l, m)- distance

from one point on a wave to the same point repeatingCrest- high point on a waveTrough- 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

Wave SpeedSpeed (m/s)- v=l/T

Phase (q)- the displacement of one wave’s peak from another’s peak100% In phase- peaks match up100% out of phase- peak matches up to trough

Amplitude- height from equilibrium to peak

14.3 Wave BehaviorWaves at Boundaries

Boundary- a change in medium Air to water, stiff spring to soft spring, etc.

Incident wave- wave that strikes the boundaryReflected wave- the returning wave

All of the wave is not reflected, some passes through to second medium

InterferencePrinciple 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

Wave InterferenceNode- the point at which a wave doesn’t move

at allMid-point of trough and crest

Antinode- the point at which the wave moves the mostHighest part of crest or trough

Standing wave- a wave that perfectly fits the length of the objectAlways in odd multiples of ½l (l=one full wavelength)See page 389

a=(1)(½l), b=(3)(½l), c=(5)(½l)

Waves in 2DWave front- a line that

represents the crest of a waveCan be circular or straight

Ray- represents the direction of travel and is perpendicular to the wave frontAngles are measured from the

Normal to the reflection surface

Law of Reflection- the angle of incidence equals the angle of reflection

RefractionLaw of Refraction- when changing mediums,

a wave is bent (changes direction) instead of reflected

Physics Physlets I.34.1