Spring Constant, K The constant k is called the spring constant. SI unit of k = N/m.
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Transcript of Spring Constant, K The constant k is called the spring constant. SI unit of k = N/m.
Spring Constant, K
The constant k is called the spring constant.
SI unit of k = N/m.
Simple Harmonic Motion
When there is a restoring force, F = -kx, simple harmonic motion occurs.
Position VS. Time graph
Oscillating Mass
.2k
mT
Consider a mass m attached to the end of a spring as shown.
If the mass is pulled down and released, it will undergo simple harmonic motion.
The period depends on the spring constant, k and the mass m, as given below,
2
2
4kT
m
Waves
Waves are the means by which energy is transferred from one point
to another
• Medium- what the wave travels through– Ex. Water, spring, string, air
Longitudinal waves- sound waves, seismic waves or pressure waves
Transverse waves- electromagnetic waves
The displacement of the particlesThe displacement of the particlesof the medium isof the medium is perpendicularperpendicular totothe direction of wave propagation.the direction of wave propagation.
TRANSVERSETRANSVERSE
LONGITUDINALLONGITUDINAL
The displacement of the particlesThe displacement of the particlesof the mediumof the medium isis parallelparallel to theto thedirection of wave propagation.direction of wave propagation.
AmplitudeAmplitudethe the maximum displacementmaximum displacement
of a particle of the medium fromof a particle of the medium fromthe rest or equilibrium positionthe rest or equilibrium positiondenoted by A and measured in units of lengthdenoted by A and measured in units of length
PhasePhaserelated to the related to the position and motionposition and motion
of the particles of the mediumof the particles of the medium
WavelengthWavelengththe the shortest distanceshortest distance
betweenbetweentwo points that are “in two points that are “in
phase”phase”denoted by denoted by and measured in units of length and measured in units of length
FrequencyFrequency- - the number of complete the number of complete vibrations per unit timevibrations per unit time
denoted by f and measured in units of Hzdenoted by f and measured in units of Hz
PeriodPeriod - - the shortest the shortest timetime interval during interval duringwhich the motion of the wave repeats itselfwhich the motion of the wave repeats itself
denoted by T and measured in units of timedenoted by T and measured in units of time
T = 1/f
& f = 1/T
VelocityVelocity - the - the speedspeed of the wave of the wave
denoted by v and measured in units of dist/timedenoted by v and measured in units of dist/time
v = d/t = /T = f
The speed of a wave depends on the propertiesThe speed of a wave depends on the propertiesof the medium through which it is traveling.of the medium through which it is traveling.
ReflectionReflection
the the turning backturning back of a wave when of a wave whenit reaches the it reaches the boundaryboundary of the of the
medium through which it is travelingmedium through which it is traveling
the bendingbending of a wave as it passes obliquelyobliquely from
one medium into another of different propagation different propagation
speedspeed
RefractioRefractionn
For refraction to occur, the waveFor refraction to occur, the wavemust change speed and must entermust change speed and must enterthe new medium at an oblique angle.the new medium at an oblique angle.
DiffractionDiffractionthethe spreadingspreading of a of a
wavewavearound a barrier oraround a barrier orthrough an openingthrough an opening
InterferenceInterferencethe result of the the result of the superpositionsuperposition
of two or more wavesof two or more waves
Superposition PrincipleSuperposition Principle
the displacement of the medium whenthe displacement of the medium whentwo or more waves pass throughtwo or more waves pass through
it at the same time is the it at the same time is the algebraicalgebraicsumsum of the displacements caused of the displacements caused
by the individual wavesby the individual waves
ConstructiveConstructiveresults in a larger amplitudelarger amplitude
Types of InterferenceTypes of Interference
DestructiveDestructiveresults in a smaller amplitudesmaller amplitude
Read more about interference Read more about interference here..
Click Click here to view the interference to view the interferencepattern resulting from the superpositionpattern resulting from the superposition
of two transverse waves.of two transverse waves.
Click Click here and and here to viewsimulations of the interference of
two circular waves.
You can view reflection,You can view reflection,refraction, diffraction,refraction, diffraction,and interference using bothand interference using bothplane and circular waves.plane and circular waves.
Click Click here to view a movie to view a movieclip of an actual ripple tank experiment.clip of an actual ripple tank experiment.
The ripple tankThe ripple tanksimulation foundsimulation foundhere can be used can be usedto investigateto investigatewave properties.wave properties.
A standing wavestanding wave is theresult of two wave trains of the same
wavelength, frequency, and amplitudetraveling in opposite directions
through the same medium.
23
Standing Waves
• Appear to be standing still• Standing waves are caused by two
waves continuously interfering with each other.
Learn more about standing waveshere, here, and here.
Click here to view a simulation of theinterference of two traveling wavesthat can result in a standing wave.
Click here to view a simulationof standing waves on a string.
Standing waves may be produced easily inwater, string, and air columns.
Doppler EffectDoppler Effectthe change in frequency due to the relativethe change in frequency due to the relativemotion of the wave source and the observermotion of the wave source and the observer
The The observed frequencyobserved frequency is is higherhigher when when thethe
source and observer are getting source and observer are getting closercloser..
The The observed frequencyobserved frequency is is lowerlower when when thethe
source and observer are getting farther source and observer are getting farther awayaway..
Click here, here, here, and hereClick here, here, here, and hereto run simulations of the Doppler Effect.to run simulations of the Doppler Effect.
The Doppler EffectThe Doppler Effectcan be evident forcan be evident forall types of waves –all types of waves –including light,including light,sound, water, etc…sound, water, etc…