Physics of Resonance

Physics of ResonancePhysics of Resonance

The most striking and unexpected The most striking and unexpected phenomenon in all of physicsphenomenon in all of physics

An ACE Project done by:An ACE Project done by:Poon Weng Shern (22) 3O3Poon Weng Shern (22) 3O3

DefinitionDefinition Before going onto the topic of Before going onto the topic of

resonance, some terminologies have resonance, some terminologies have to be explainedto be explained

These include:These include:• Forced OscillationForced Oscillation• Natural/Driving FrequenciesNatural/Driving Frequencies

Damped (not forced) OscillationDamped (not forced) Oscillation In a spring-mass system or a In a spring-mass system or a

pendulum, what we see of the pendulum, what we see of the motion of the bob is called a Damped motion of the bob is called a Damped OscillationOscillation

The bob moves in simple harmonic The bob moves in simple harmonic motion, that is subjected to frictional motion, that is subjected to frictional and dissipative forcesand dissipative forces

Total amount of energy decreases Total amount of energy decreases over timeover time

http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/SHM/TwoSHM.html

Damping OscillationDamping Oscillation Here is how a graph of the total Here is how a graph of the total

amount of energy over time should amount of energy over time should look like, look like,

Forced OscillationForced Oscillation A forced oscillation happens when an A forced oscillation happens when an

external force is applied external force is applied to to compensate for energy loss in a compensate for energy loss in a damped systemdamped system

Natural FrequencyNatural Frequency Now moving on,Now moving on, Any system performing simple Any system performing simple

harmonic motion that oscillates harmonic motion that oscillates about the equilibrium position is said about the equilibrium position is said to have a natural frequencyto have a natural frequency

That is a fixed value of number of That is a fixed value of number of oscillations per secondoscillations per second

Driving FrequencyDriving Frequency As said earlier, a forced oscillation is As said earlier, a forced oscillation is

when an external force is appliedwhen an external force is applied This external driving force that This external driving force that

replenishes the energy of an replenishes the energy of an oscillating system also has a oscillating system also has a frequencyfrequency

Driving Force appletDriving Force applet In the next slide, it will show how a driving frequency will In the next slide, it will show how a driving frequency will

affect the natural frequency of the oscilliating objectaffect the natural frequency of the oscilliating object

Try this:Try this: 1. Adjust the damping constant to 0.1. Adjust the damping constant to 0.

2. Then adjust the natural frequency to maximum, which is 2. Then adjust the natural frequency to maximum, which is about 0.40Hz. Observe how the motion of the mass will look about 0.40Hz. Observe how the motion of the mass will look likelike

3. Then, press the rewind button, and change the natural 3. Then, press the rewind button, and change the natural frequency to 0.20Hz, which is the same as the driving frequency to 0.20Hz, which is the same as the driving frequency. Observe how the motion of the mass has frequency. Observe how the motion of the mass has changedchanged

For exampleFor example

http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/DrivenSHM/DrivenSHM.html

ResultsResults You will notice thatYou will notice that1.1. At natural frequency of 0.40Hz, the At natural frequency of 0.40Hz, the

motion of the mass fluctuates, but motion of the mass fluctuates, but the distance is often not farthe distance is often not far

2.2. At natural frequency of 0.20Hz, the At natural frequency of 0.20Hz, the motion of the mass increases after motion of the mass increases after each wavelength, that finally the each wavelength, that finally the mass flies off the elevated landmass flies off the elevated land

This is known as an unusual This is known as an unusual phenomenon calledphenomenon called

ResonanceResonance

ResonanceResonance Takes place when the driving Takes place when the driving

frequency of the external oscillatory frequency of the external oscillatory force is force is equalequal to the natural to the natural frequency of the oscillating systemfrequency of the oscillating system

Thus the energy received by the Thus the energy received by the mass is at maximum, and so the mass is at maximum, and so the system will oscillate at maximum system will oscillate at maximum amplitudeamplitude

Examples of ResonanceExamples of Resonance This can be seen when This can be seen when

sitting in a bus or vansitting in a bus or van When the vehicle is When the vehicle is

stationary, the people will stationary, the people will often feel that the bus is often feel that the bus is shaking very violently and shaking very violently and vibrating vigorouslyvibrating vigorously

However, when the vehicle However, when the vehicle is moving, the shaking gets is moving, the shaking gets less violentless violent

This is because when the vehicle is stationary, This is because when the vehicle is stationary, frequency of the engine vibration is slow. It equals to frequency of the engine vibration is slow. It equals to the natural frequency of the cab of the vehicle, thus the natural frequency of the cab of the vehicle, thus resonance occursresonance occurs

There is maximum amplitude of vibrations – violent There is maximum amplitude of vibrations – violent vibrationsvibrations

However, when the lorry is moving faster, frequency However, when the lorry is moving faster, frequency of engine vibrations increase, and is much faster than of engine vibrations increase, and is much faster than the natural frequency of the engine, thus no resonance the natural frequency of the engine, thus no resonance occursoccurs

Another example to illustrate Another example to illustrate resonanceresonance

Pushing a person in a swing in time with Pushing a person in a swing in time with the natural interval of the swing (its the natural interval of the swing (its resonant frequency) will make the swing resonant frequency) will make the swing go higher and higher (maximum go higher and higher (maximum amplitude), while attempts to push the amplitude), while attempts to push the swing at a faster or slower tempo will swing at a faster or slower tempo will result in smaller arcs. result in smaller arcs.

This is because the energy the swing This is because the energy the swing absorbs is maximized when the absorbs is maximized when the pushes are 'in phase' with the pushes are 'in phase' with the swing's oscillations, while some of swing's oscillations, while some of the swing's energy is actually the swing's energy is actually extracted by the opposing force of extracted by the opposing force of the pushes when they are not. the pushes when they are not.

Useful applications of ResonanceUseful applications of Resonance

Microwave ovensMicrowave ovens

• Heat up food throughHeat up food throughradiation/ electromagnetic radiation/ electromagnetic waveswaves• Food mainly gets heated up due to the Food mainly gets heated up due to the

absorption of heat energy in the water absorption of heat energy in the water molecules in the foodmolecules in the food

Useful applications of ResonanceUseful applications of Resonance

• The frequency of microwaves The frequency of microwaves corresponds to the natural frequency of corresponds to the natural frequency of water molecules. water molecules.

• The water molecules in the food placed The water molecules in the food placed in the microwave oven resonate when in the microwave oven resonate when subjected to microwaves. subjected to microwaves.

• Thus, they absorb energy and Thus, they absorb energy and consequently heat up the food, enabling consequently heat up the food, enabling the food to be cookedthe food to be cooked

Useful applications of ResonanceUseful applications of Resonance

Radios (Electronic Resonance)Radios (Electronic Resonance)• In order to tune in to a particular radio In order to tune in to a particular radio

station, adjust the natural frequency of station, adjust the natural frequency of the electrical receiving circuit in the the electrical receiving circuit in the radio to match that of the frequency of radio to match that of the frequency of radio waves emitted by the station. radio waves emitted by the station.

• Resonance is thus used to isolate and Resonance is thus used to isolate and amplify the required frequency.amplify the required frequency.

Useful applications of ResonanceUseful applications of Resonance

Magnetic ResonanceMagnetic Resonance• Strong, varying radio frequency Strong, varying radio frequency

electromagnetic fields are used to cause electromagnetic fields are used to cause the nuclei of atoms to oscillate.the nuclei of atoms to oscillate.

• In any given molecule, there will be In any given molecule, there will be many resonant frequencies. Energy is many resonant frequencies. Energy is absorbed whenever resonance appears. absorbed whenever resonance appears.

• The pattern of energy The pattern of energy absorption can be used absorption can be used to detect the presence of to detect the presence of particular molecules particular molecules within any specimenwithin any specimen

• False colour magnetic False colour magnetic resonance image on the resonance image on the right shows woman’s right shows woman’s abdomen at 8 months of abdomen at 8 months of pregnancy pregnancy

Harmful effects of ResonanceHarmful effects of Resonance Vibrations of bridge structuresVibrations of bridge structures

• Bridges especially suspension bridges Bridges especially suspension bridges are exposed to variable amounts and are exposed to variable amounts and frequencies of wind everydayfrequencies of wind everyday

• Bridges have multiple natural Bridges have multiple natural frequencies, therefore as long as there frequencies, therefore as long as there is 1 driving frequency equal to the is 1 driving frequency equal to the natural frequency of the bridge, it may natural frequency of the bridge, it may possible rupture itpossible rupture it

Case Study: Case Study: 1940 1940 Tacoma Narrows suspension bridge Tacoma Narrows suspension bridge

accidentaccident

http://www.youtube.com/watch?v=P0Fi1VcbpAI

What happened?What happened? Wind, in this case, was the driving Wind, in this case, was the driving

oscillating force that matched the oscillating force that matched the natural frequency of the bridgenatural frequency of the bridge

This caused huge vibrations and This caused huge vibrations and amplitudes built up, which eventually amplitudes built up, which eventually put stress on the concrete, thus put stress on the concrete, thus rupturing itrupturing it

Another caseAnother case Besides wind, there was also another Besides wind, there was also another

peculiar incident that happened on a peculiar incident that happened on a bridgebridge

In 1831, a French battalion was In 1831, a French battalion was marching over a suspension bridge in marching over a suspension bridge in AngersAngers

The bridge collapsed due to large The bridge collapsed due to large amplitude of oscillations built up in amplitude of oscillations built up in the system when the rhythm of the the system when the rhythm of the marching steps matches the natural marching steps matches the natural frequency of vibration of the bridgefrequency of vibration of the bridge

Since then, it has been common Since then, it has been common practice to order soldiers to break practice to order soldiers to break steps when crossing a bridge.steps when crossing a bridge.

In the moviesIn the movies Many films that involve soprano Many films that involve soprano

singers try to be comical by breaking singers try to be comical by breaking glass walls due to their high pitchglass walls due to their high pitch

So is this real?So is this real?

Video of Breaking a wineglass with Video of Breaking a wineglass with nothing but soundnothing but sound

It has been known that high-pitched It has been known that high-pitched sound waves shatter fragile objects. sound waves shatter fragile objects.

This is because sound resonance has This is because sound resonance has occurred, when the high frequency occurred, when the high frequency sound waves are equal to the natural sound waves are equal to the natural frequency of the wineglassfrequency of the wineglass

Amusing, but trueAmusing, but true

Thank you for watching my Thank you for watching my presentation slides.presentation slides.

ReflectionsReflections One major misconception I One major misconception I

encountered in this ACE project, was encountered in this ACE project, was to mistake frequency with to mistake frequency with wavelengthwavelength

So, I thought that resonance was the So, I thought that resonance was the occurrence of a driving force which is occurrence of a driving force which is equal to the force of the original equal to the force of the original object was appliedobject was applied

SourcesSources Jearl Walker, David Halliday, and Robert Jearl Walker, David Halliday, and Robert

Resnick.Resnick.Fundamentals of Physics Extended, 8th EditionFundamentals of Physics Extended, 8th Edition. 8th . 8th ed. United States of America: Wiley, 2008. 408-12. eBook. ed. United States of America: Wiley, 2008. 408-12. eBook. http://www.physicsclassroom.com/class/sound/u11l4a.cfmhttp://www.physicsclassroom.com/class/sound/u11l4a.cfm

http://www.physicsclassroom.com/class/sound/u11l5a.cfmhttp://www.physicsclassroom.com/class/sound/u11l5a.cfm http://en.wikipedia.org/wiki/Resonancehttp://en.wikipedia.org/wiki/Resonance http://http://www.gallawa.com/microtech/howcook.htmlwww.gallawa.com/microtech/howcook.html http://www.upscale.utoronto.ca/PVB/Harrison/Flash/http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ http://en.wikipedia.org/wiki/Broughton_Suspension_Bridgehttp://en.wikipedia.org/wiki/Broughton_Suspension_Bridge http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)

ReferencesReferences http://www.alentum.com/agrapher/Damposc.gifhttp://www.alentum.com/agrapher/Damposc.gif http://en.wikipedia.org/wiki/http://en.wikipedia.org/wiki/

File:Little_girl_on_swing.jpgFile:Little_girl_on_swing.jpg http://static.howstuffworks.com/gif/car-cooking-http://static.howstuffworks.com/gif/car-cooking-

1.jpg1.jpg http://tvbythenumbers.com/wp-content/uploads/http://tvbythenumbers.com/wp-content/uploads/

2009/12/satellite.jpg2009/12/satellite.jpg http://tvbythenumbers.com/wp-content/uploads/http://tvbythenumbers.com/wp-content/uploads/

2009/12/satellite.jpg2009/12/satellite.jpg http://en.wikipedia.org/wiki/File:Broughton-http://en.wikipedia.org/wiki/File:Broughton-

suspension-bridge.jpgsuspension-bridge.jpg