Chapter 14: Vibrations & Waves
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Transcript of Chapter 14: Vibrations & Waves
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