==Resonance==
Resonance is the physical phenomenon in which a system vibrates in response to an applied frequency, but the external force of this frequency interacts with the object in such a way that it causes the system to oscillate with a maximum amplitude due to the specific frequency induced. This property applies to many fields of physics when studying the way an object behaves in certain situations.
===Natural Frequencies===
When dealing with sound and its interaction with various objects in space, a resonant frequency of a wave is the natural frequency of vibration determined by the physical and chemical properties of said object.The existence of resonance in and of itself depends on the existence of natural frequencies. Objects often have multiple natural vibrating resonant frequencies, and it will pick out those frequencies from a series of excitations, making it an even more useful tool when identifying the properties of an object.
===History===
One of the most famous visible examples of resonance in history is the disaster at the Tacoma Narrows Bridge in 1940. This bridge, in Tacoma, Washington, spanned the Tacoma Narrows Strait, but it collapsed into the waters of Puget Sound on November 7, 1940. [[File:Tacoma-narrows-bridge-collapse.jpg|thumb|This is the bridge during its collapse in 1940.]]This bridge had such a short lived existence due to resonance. Since its construction, workers observed vertical movement in the suspension bridge on windy days. This brought about the origin of the bridge's nickname: "Galloping Gertie". However, on a particularly windy day, the wind provided the bridge with a periodic vibrating frequency that matched the bridge's natural vibrational frequency, causing the bridge to become a massive oscillating standing wave. This intense oscillation proved too much for the structural integrity of the bridge, and it collapsed. No human lives were lost in the accident, but a black, male cocker spaniel named Tubby passed away from the incident.
==Standing Waves==
Studying resonance requires knowledge of what a standing wave is and how it behaves because resonance within objects have patterns of this nature. A standing wave is formed when two waves propagate through a medium and experiences both constructive and destructive interference with each other when reverberating off of a barrier. [[File:StandingWave.png|thumb|left|This is a standing wave with labeled nodes and antinodes]] This interference causes some areas of the medium to always appear still, while other areas of the medium are oscillating. These areas are called nodes and antinodes. A node is the term used to describe a place where the medium does not move due to the vibration. On the other hand, an antinode is the point where the maximum displacement of the medium occurs due to the vibration of the wave. An important characteristic of a standing wave is that when the wave reaches a fixed barrier at the end of the propagation medium, it changes phase and travels in the reverse direction instead of continuing forward. In that, a change in phase means a 180 degree transformation in the period of the wave. This can be more easily understood when viewed in the visuals provided below.

==Harmonics==
Wave patterns occur in specific manners based on the certain frequency applied. The frequencies of the wave and their relative patterns are called harmonics. Harmonics behave in a way that provides a convenient mathematical model based on the wavelength of the wave, the harmonic type, and the length of the medium it is propagating through. [[File:1Harmonics.jpg|thumb| First (Fundamental), second, third, fourth, and fifth Harmonics.]] The first harmonic consists of a single antinode in the middle of the medium, and this antinode oscillates up and down continuously. Next, the second harmonic creates two antinodes and three nodes. A full wavelength can be observed here. The third harmonic consists of three antinodes and four nodes. From these progressive patterns, a mathematical relationship can be derived to calculate the length of medium based on the wavelength of the wave. This relationship can be seen below.
===A Mathematical Model===
First Harmonic - <math> L = \frac{1}{2} * \lambda </math>

Second Harmonic - <math> L = \frac{2}{2} * \lambda </math>

Third Harmonic - <math> L = \frac{3}{2} * \lambda </math>

Fourth Harmonic - <math> L = \frac{4}{2} * \lambda </math>

.

.

.

nth Harmonic - <math> L = \frac{n}{2} * \lambda </math>

===Open Cylinder===
In an open air cylinder, waves can create all harmonics. The position of the nodes inside the tube are reversed compared to the propagation of the wave on a string. This means that for the first fundamental frequency, the node will be located at the center of the tube whereas in a string there would be two nodes, one at each end. This pattern continues for the rest of the harmonics. The Resonant frequency of the air column depends on the speed of sound in the air as well as the geometry of the air column.
===Closed Cylinder===
Different from open air tubes, a closed air column only produces resonant frequencies at the odd harmonics. Because the closed end of the tube is always a node of the wave, the open end will therefore be an antinode. This results in the fact that the wavelength of the wave is always four times the length of the tube. A good example of this concept is in the clarinet. This instrument is made of a closed cylinder, so its upper and lower registers sound much different than instruments of the woodwind family being made of open cylinders.
==Applications==
The concept of standing waves can be applied to many aspect of everyday life. Many of these applications fall in the world of music. Strings on instruments and the use of tuning forks are two very important applications of resonance and standing waves.
===Strings===
As discussed above, strings behave like standing waves when plucked or strummed on a stringed instrument like a guitar. When a guitar string is plucked though, it produces a unique sound without the player specifying. This pitch is the resonant frequency of that particular string. The pitch of the string is a result of its length, mass, and tension. Therefore, on a guitar, altering the tension of a string (tuning the guitar) allows the player to alter the resonant frequency and pitch when that string is played.

===Tuning Forks===
Tuning forks have a stable, consistent pitch when struck, and they have been used to tune instruments since the 17th century. [[File:tuning.jpg|thumb|left|This is a tuning fork.]] These tools make use of resonance because then struck on a surface, the tines (the prongs of the fork) vibrate at the same frequency in opposite directions to produce a tone. Since the tines move in opposite directions, the vibrations it creates interfere, making a standing wave unique to each individual tuning fork. With this, a musician can match a note on his or her respective instrument to the tone produced by the fork and tune their instrument from there.

==Connectedness==

==See Also==
[[Nature, Behavior, and Properties of Sound]]

[[Doppler Effect]]

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

[[Sound]]

File:Tuning.jpg

2015-11-30T00:00:40Z

Rtrickett3:

Resonance

2015-11-29T23:59:24Z

Rtrickett3: /* Tuning Forks */

==Resonance==
Resonance is the physical phenomenon in which a system vibrates in response to an applied frequency, but the external force of this frequency interacts with the object in such a way that it causes the system to oscillate with a maximum amplitude due to the specific frequency induced. This property applies to many fields of physics when studying the way an object behaves in certain situations.
===Natural Frequencies===
When dealing with sound and its interaction with various objects in space, a resonant frequency of a wave is the natural frequency of vibration determined by the physical and chemical properties of said object.The existence of resonance in and of itself depends on the existence of natural frequencies. Objects often have multiple natural vibrating resonant frequencies, and it will pick out those frequencies from a series of excitations, making it an even more useful tool when identifying the properties of an object.
===History===
One of the most famous visible examples of resonance in history is the disaster at the Tacoma Narrows Bridge in 1940. This bridge, in Tacoma, Washington, spanned the Tacoma Narrows Strait, but it collapsed into the waters of Puget Sound on November 7, 1940. [[File:Tacoma-narrows-bridge-collapse.jpg|thumb|This is the bridge during its collapse in 1940.]]This bridge had such a short lived existence due to resonance. Since its construction, workers observed vertical movement in the suspension bridge on windy days. This brought about the origin of the bridge's nickname: "Galloping Gertie". However, on a particularly windy day, the wind provided the bridge with a periodic vibrating frequency that matched the bridge's natural vibrational frequency, causing the bridge to become a massive oscillating standing wave. This intense oscillation proved too much for the structural integrity of the bridge, and it collapsed. No human lives were lost in the accident, but a black, male cocker spaniel named Tubby passed away from the incident.
==Standing Waves==
Studying resonance requires knowledge of what a standing wave is and how it behaves because resonance within objects have patterns of this nature. A standing wave is formed when two waves propagate through a medium and experiences both constructive and destructive interference with each other when reverberating off of a barrier. [[File:StandingWave.png|thumb|left|This is a standing wave with labeled nodes and antinodes]] This interference causes some areas of the medium to always appear still, while other areas of the medium are oscillating. These areas are called nodes and antinodes. A node is the term used to describe a place where the medium does not move due to the vibration. On the other hand, an antinode is the point where the maximum displacement of the medium occurs due to the vibration of the wave. An important characteristic of a standing wave is that when the wave reaches a fixed barrier at the end of the propagation medium, it changes phase and travels in the reverse direction instead of continuing forward. In that, a change in phase means a 180 degree transformation in the period of the wave. This can be more easily understood when viewed in the visuals provided below.

==Harmonics==
Wave patterns occur in specific manners based on the certain frequency applied. The frequencies of the wave and their relative patterns are called harmonics. Harmonics behave in a way that provides a convenient mathematical model based on the wavelength of the wave, the harmonic type, and the length of the medium it is propagating through. [[File:1Harmonics.jpg|thumb| First (Fundamental), second, third, fourth, and fifth Harmonics.]] The first harmonic consists of a single antinode in the middle of the medium, and this antinode oscillates up and down continuously. Next, the second harmonic creates two antinodes and three nodes. A full wavelength can be observed here. The third harmonic consists of three antinodes and four nodes. From these progressive patterns, a mathematical relationship can be derived to calculate the length of medium based on the wavelength of the wave. This relationship can be seen below.
===A Mathematical Model===
First Harmonic - <math> L = \frac{1}{2} * \lambda </math>

Second Harmonic - <math> L = \frac{2}{2} * \lambda </math>

Third Harmonic - <math> L = \frac{3}{2} * \lambda </math>

Fourth Harmonic - <math> L = \frac{4}{2} * \lambda </math>

.

.

.

nth Harmonic - <math> L = \frac{n}{2} * \lambda </math>

===Open Cylinder===
In an open air cylinder, waves can create all harmonics. The position of the nodes inside the tube are reversed compared to the propagation of the wave on a string. This means that for the first fundamental frequency, the node will be located at the center of the tube whereas in a string there would be two nodes, one at each end. This pattern continues for the rest of the harmonics. The Resonant frequency of the air column depends on the speed of sound in the air as well as the geometry of the air column.
===Closed Cylinder===
Different from open air tubes, a closed air column only produces resonant frequencies at the odd harmonics. Because the closed end of the tube is always a node of the wave, the open end will therefore be an antinode. This results in the fact that the wavelength of the wave is always four times the length of the tube. A good example of this concept is in the clarinet. This instrument is made of a closed cylinder, so its upper and lower registers sound much different than instruments of the woodwind family being made of open cylinders.
==Applications==
The concept of standing waves can be applied to many aspect of everyday life. Many of these applications fall in the world of music. Strings on instruments and the use of tuning forks are two very important applications of resonance and standing waves.
===Strings===
As discussed above, strings behave like standing waves when plucked or strummed on a stringed instrument like a guitar. When a guitar string is plucked though, it produces a unique sound without the player specifying. This pitch is the resonant frequency of that particular string. The pitch of the string is a result of its length, mass, and tension. Therefore, on a guitar, altering the tension of a string (tuning the guitar) allows the player to alter the resonant frequency and pitch when that string is played.

===Tuning Forks===
Tuning forks have a stable, consistent pitch when struck, and they have been used to tune instruments since the 17th century. [[File:tuningfork.jpg|thumb|left|This is a tuning fork.]] These tools make use of resonance because then struck on a surface, the tines (the prongs of the fork) vibrate at the same frequency in opposite directions to produce a tone. Since the tines move in opposite directions, the vibrations it creates interfere, making a standing wave unique to each individual tuning fork. With this, a musician can match a note on his or her respective instrument to the tone produced by the fork and tune their instrument from there.

==Connectedness==

==See Also==
[[Nature, Behavior, and Properties of Sound]]

[[Doppler Effect]]

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

[[Sound]]

Resonance

2015-11-29T23:58:59Z

Rtrickett3: /* Tuning Forks */

==Resonance==
Resonance is the physical phenomenon in which a system vibrates in response to an applied frequency, but the external force of this frequency interacts with the object in such a way that it causes the system to oscillate with a maximum amplitude due to the specific frequency induced. This property applies to many fields of physics when studying the way an object behaves in certain situations.
===Natural Frequencies===
When dealing with sound and its interaction with various objects in space, a resonant frequency of a wave is the natural frequency of vibration determined by the physical and chemical properties of said object.The existence of resonance in and of itself depends on the existence of natural frequencies. Objects often have multiple natural vibrating resonant frequencies, and it will pick out those frequencies from a series of excitations, making it an even more useful tool when identifying the properties of an object.
===History===
One of the most famous visible examples of resonance in history is the disaster at the Tacoma Narrows Bridge in 1940. This bridge, in Tacoma, Washington, spanned the Tacoma Narrows Strait, but it collapsed into the waters of Puget Sound on November 7, 1940. [[File:Tacoma-narrows-bridge-collapse.jpg|thumb|This is the bridge during its collapse in 1940.]]This bridge had such a short lived existence due to resonance. Since its construction, workers observed vertical movement in the suspension bridge on windy days. This brought about the origin of the bridge's nickname: "Galloping Gertie". However, on a particularly windy day, the wind provided the bridge with a periodic vibrating frequency that matched the bridge's natural vibrational frequency, causing the bridge to become a massive oscillating standing wave. This intense oscillation proved too much for the structural integrity of the bridge, and it collapsed. No human lives were lost in the accident, but a black, male cocker spaniel named Tubby passed away from the incident.
==Standing Waves==
Studying resonance requires knowledge of what a standing wave is and how it behaves because resonance within objects have patterns of this nature. A standing wave is formed when two waves propagate through a medium and experiences both constructive and destructive interference with each other when reverberating off of a barrier. [[File:StandingWave.png|thumb|left|This is a standing wave with labeled nodes and antinodes]] This interference causes some areas of the medium to always appear still, while other areas of the medium are oscillating. These areas are called nodes and antinodes. A node is the term used to describe a place where the medium does not move due to the vibration. On the other hand, an antinode is the point where the maximum displacement of the medium occurs due to the vibration of the wave. An important characteristic of a standing wave is that when the wave reaches a fixed barrier at the end of the propagation medium, it changes phase and travels in the reverse direction instead of continuing forward. In that, a change in phase means a 180 degree transformation in the period of the wave. This can be more easily understood when viewed in the visuals provided below.

==Harmonics==
Wave patterns occur in specific manners based on the certain frequency applied. The frequencies of the wave and their relative patterns are called harmonics. Harmonics behave in a way that provides a convenient mathematical model based on the wavelength of the wave, the harmonic type, and the length of the medium it is propagating through. [[File:1Harmonics.jpg|thumb| First (Fundamental), second, third, fourth, and fifth Harmonics.]] The first harmonic consists of a single antinode in the middle of the medium, and this antinode oscillates up and down continuously. Next, the second harmonic creates two antinodes and three nodes. A full wavelength can be observed here. The third harmonic consists of three antinodes and four nodes. From these progressive patterns, a mathematical relationship can be derived to calculate the length of medium based on the wavelength of the wave. This relationship can be seen below.
===A Mathematical Model===
First Harmonic - <math> L = \frac{1}{2} * \lambda </math>

Second Harmonic - <math> L = \frac{2}{2} * \lambda </math>

Third Harmonic - <math> L = \frac{3}{2} * \lambda </math>

Fourth Harmonic - <math> L = \frac{4}{2} * \lambda </math>

.

.

.

nth Harmonic - <math> L = \frac{n}{2} * \lambda </math>

===Open Cylinder===
In an open air cylinder, waves can create all harmonics. The position of the nodes inside the tube are reversed compared to the propagation of the wave on a string. This means that for the first fundamental frequency, the node will be located at the center of the tube whereas in a string there would be two nodes, one at each end. This pattern continues for the rest of the harmonics. The Resonant frequency of the air column depends on the speed of sound in the air as well as the geometry of the air column.
===Closed Cylinder===
Different from open air tubes, a closed air column only produces resonant frequencies at the odd harmonics. Because the closed end of the tube is always a node of the wave, the open end will therefore be an antinode. This results in the fact that the wavelength of the wave is always four times the length of the tube. A good example of this concept is in the clarinet. This instrument is made of a closed cylinder, so its upper and lower registers sound much different than instruments of the woodwind family being made of open cylinders.
==Applications==
The concept of standing waves can be applied to many aspect of everyday life. Many of these applications fall in the world of music. Strings on instruments and the use of tuning forks are two very important applications of resonance and standing waves.
===Strings===
As discussed above, strings behave like standing waves when plucked or strummed on a stringed instrument like a guitar. When a guitar string is plucked though, it produces a unique sound without the player specifying. This pitch is the resonant frequency of that particular string. The pitch of the string is a result of its length, mass, and tension. Therefore, on a guitar, altering the tension of a string (tuning the guitar) allows the player to alter the resonant frequency and pitch when that string is played.

===Tuning Forks===
Tuning forks have a stable, consistent pitch when struck, and they have been used to tune instruments since the 17th century. [[File:tuningfork.png|thumb|left|This is a tuning fork.]] These tools make use of resonance because then struck on a surface, the tines (the prongs of the fork) vibrate at the same frequency in opposite directions to produce a tone. Since the tines move in opposite directions, the vibrations it creates interfere, making a standing wave unique to each individual tuning fork. With this, a musician can match a note on his or her respective instrument to the tone produced by the fork and tune their instrument from there.

==Connectedness==

==See Also==
[[Nature, Behavior, and Properties of Sound]]

[[Doppler Effect]]

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

[[Sound]]

Resonance

2015-11-29T21:01:33Z

Rtrickett3:

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Terminal Velocity and Friction Due to Air]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Josiah Willard Gibbs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting a Change in Rotation]]
* [[Conservation of Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[Total Angular Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
*[[Internal Energy]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
*[[Faraday's Law]]
**[[Inductance]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
*[[Ampere-Maxwell Law]]
**[[Superconducters]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Standing Waves]]
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]