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.

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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…