Physics of Resonance The most striking and unexpected phenomenon in all of physics An ACE Project done by: Poon Weng Shern (22) 3O3

Definition  Before going onto the topic of resonance, some terminologies have to be explained  These include: Forced OscillationForced Oscillation Natural/Driving FrequenciesNatural/Driving Frequencies

Damped (not forced) Oscillation  In a spring-mass system or a pendulum, what we see of the motion of the bob is called a Damped Oscillation  The bob moves in simple harmonic motion, that is subjected to frictional and dissipative forces  Total amount of energy decreases over time

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Damping Oscillation  Here is how a graph of the total amount of energy over time should look like,

Forced Oscillation  A forced oscillation happens when an external force is applied to compensate for energy loss in a damped system

Natural Frequency  Now moving on,  Any system performing simple harmonic motion that oscillates about the equilibrium position is said to have a natural frequency  That is a fixed value of number of oscillations per second

Driving Frequency  As said earlier, a forced oscillation is when an external force is applied  This external driving force that replenishes the energy of an oscillating system also has a frequency

Driving Force applet  In the next slide, it will show how a driving frequency will affect the natural frequency of the oscilliating object  Try this:  1. Adjust the damping constant to 0.  2. Then adjust the natural frequency to maximum, which is about 0.40Hz. Observe how the motion of the mass will look like  3. Then, press the rewind button, and change the natural frequency to 0.20Hz, which is the same as the driving frequency. Observe how the motion of the mass has changed

For example

Results  You will notice that 1. At natural frequency of 0.40Hz, the motion of the mass fluctuates, but the distance is often not far 2. At natural frequency of 0.20Hz, the motion of the mass increases after each wavelength, that finally the mass flies off the elevated land

This is known as an unusual phenomenon called Resonance

Resonance  Takes place when the driving frequency of the external oscillatory force is equal to the natural frequency of the oscillating system  Thus the energy received by the mass is at maximum, and so the system will oscillate at maximum amplitude

Examples of Resonance  This can be seen when sitting in a bus or van  When the vehicle is stationary, the people will often feel that the bus is shaking very violently and vibrating vigorously  However, when the vehicle is moving, the shaking gets less violent

 This is because when the vehicle is stationary, frequency of the engine vibration is slow. It equals to the natural frequency of the cab of the vehicle, thus resonance occurs  There is maximum amplitude of vibrations – violent vibrations  However, when the lorry is moving faster, frequency of engine vibrations increase, and is much faster than the natural frequency of the engine, thus no resonance occurs

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

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

Useful applications of Resonance  Microwave ovens Heat up food throughHeat up food through radiation/ electromagnetic waves Food mainly gets heated up due to the absorption of heat energy in the water molecules in the food Food mainly gets heated up due to the absorption of heat energy in the water molecules in the food

Useful applications of Resonance The frequency of microwaves corresponds to the natural frequency of water molecules.The frequency of microwaves corresponds to the natural frequency of water molecules. The water molecules in the food placed in the microwave oven resonate when subjected to microwaves.The water molecules in the food placed in the microwave oven resonate when subjected to microwaves. Thus, they absorb energy and consequently heat up the food, enabling the food to be cookedThus, they absorb energy and consequently heat up the food, enabling the food to be cooked

Useful applications of Resonance  Radios (Electronic Resonance) In order to tune in to a particular radio station, adjust the natural frequency of the electrical receiving circuit in the radio to match that of the frequency of radio waves emitted by the station.In order to tune in to a particular radio station, adjust the natural frequency of the electrical receiving circuit in the radio to match that of the frequency of radio waves emitted by the station. Resonance is thus used to isolate and amplify the required frequency.Resonance is thus used to isolate and amplify the required frequency.

Useful applications of Resonance  Magnetic Resonance Strong, varying radio frequency electromagnetic fields are used to cause the nuclei of atoms to oscillate.Strong, varying radio frequency electromagnetic fields are used to cause the nuclei of atoms to oscillate. In any given molecule, there will be many resonant frequencies. Energy is absorbed whenever resonance appears.In any given molecule, there will be many resonant frequencies. Energy is absorbed whenever resonance appears.

The pattern of energy absorption can be used to detect the presence of particular molecules within any specimenThe pattern of energy absorption can be used to detect the presence of particular molecules within any specimen False colour magnetic resonance image on the right shows woman’s abdomen at 8 months of pregnancyFalse colour magnetic resonance image on the right shows woman’s abdomen at 8 months of pregnancy

Harmful effects of Resonance  Vibrations of bridge structures Bridges especially suspension bridges are exposed to variable amounts and frequencies of wind everydayBridges especially suspension bridges are exposed to variable amounts and frequencies of wind everyday Bridges have multiple natural frequencies, therefore as long as there is 1 driving frequency equal to the natural frequency of the bridge, it may possible rupture itBridges have multiple natural frequencies, therefore as long as there is 1 driving frequency equal to the natural frequency of the bridge, it may possible rupture it

Case Study: 1940 Tacoma Narrows suspension bridge accident

What happened?  Wind, in this case, was the driving oscillating force that matched the natural frequency of the bridge  This caused huge vibrations and amplitudes built up, which eventually put stress on the concrete, thus rupturing it

Another case  Besides wind, there was also another peculiar incident that happened on a bridge  In 1831, a French battalion was marching over a suspension bridge in Angers

 The bridge collapsed due to large amplitude of oscillations built up in the system when the rhythm of the marching steps matches the natural frequency of vibration of the bridge  Since then, it has been common practice to order soldiers to break steps when crossing a bridge.

In the movies  Many films that involve soprano singers try to be comical by breaking glass walls due to their high pitch  So is this real?

Video of Breaking a wineglass with nothing but sound

 It has been known that high-pitched sound waves shatter fragile objects.  This is because sound resonance has occurred, when the high frequency sound waves are equal to the natural frequency of the wineglass

 Amusing, but true  Thank you for watching my presentation slides.

Reflections  One major misconception I encountered in this ACE project, was to mistake frequency with wavelength  So, I thought that resonance was the occurrence of a driving force which is equal to the force of the original object was applied

Sources  Jearl Walker, David Halliday, and Robert Resnick.Fundamentals of Physics Extended, 8th Edition. 8th ed. United States of America: Wiley, eBook.       0) 0) 0)

References   wing.jpg wing.jpg wing.jpg  1.jpg 1.jpg 1.jpg  content/uploads/2009/12/satellite.jpg content/uploads/2009/12/satellite.jpg content/uploads/2009/12/satellite.jpg  content/uploads/2009/12/satellite.jpg content/uploads/2009/12/satellite.jpg content/uploads/2009/12/satellite.jpg  suspension-bridge.jpg suspension-bridge.jpg suspension-bridge.jpg