Difference between revisions of "Crave the Wave"

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:[[#Wave Phenomena|'''Wave Phenomena''']]
 
:[[#Wave Phenomena|'''Wave Phenomena''']]
 
:[[#Electromagnetic Spectrum|'''Electromagnetic Waves''']] Insert info on: energy carried (AM/FM only), standard wavelength bands, their uses and dangers, how the electromagnetic spectrum relates to everyday life, and mechanical and electromagnetic waves.  
 
:[[#Electromagnetic Spectrum|'''Electromagnetic Waves''']] Insert info on: energy carried (AM/FM only), standard wavelength bands, their uses and dangers, how the electromagnetic spectrum relates to everyday life, and mechanical and electromagnetic waves.  
−
:[[#Spectroscopy|'''Spectroscopy''']]: [[#Filters|Filters]] and [[#Colors|Primary colors]] Insert info on: Spectroscopy, absorption and emission spectra and their purpose in astronomy
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:[[#Spectroscopy|'''Spectroscopy''']]: [[#Filters|Filters]] and [[#Colors|Primary colors]]
  
 
Some calculations are required, such as calculation of frequency, period, wavelength, and speed.  
 
Some calculations are required, such as calculation of frequency, period, wavelength, and speed.  
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[[File:1280px-EM Spectrum Properties edit svg.png|600px]]
 
[[File:1280px-EM Spectrum Properties edit svg.png|600px]]
 
[[File:Untitled1.png|500px]]
 
[[File:Untitled1.png|500px]]
−
The electromagnetic field is a combination of the magnetic field and the electric field. All EM waves are transverse in nature. They all travel at the speed of light, <math>c = 3.00 \times 10^8 \frac{m}{s}</math>. That means <math>\lambda \propto \frac{1}{f}</math>, as <math>v = \lambda f</math> and <math>v = 3.00 \times 10^8 \frac{m}{s}</math>. The photon energy of a wave is measured in joules and electron volts and can be calculated as follows: <math>e = hf = \frac{ch}{\lambda}</math> where h = Planck's constant = <math>6.62607 \times 10^{-34} Js</math>. Radio waves are the waves with the least energy, longest wavelength, and smallest frequency. These can be split up into AM waves, FM waves, short radio waves, telemetry/millimeter-waves, and terahertz waves. Next are microwaves which are used in microwaves to heat food and infrared waves which humans emit. After that are visible light waves which things like lava emit. Ultraviolet rays are next. Then come x-rays and gamma rays which have the highest energies.
+
The electromagnetic field is a combination of the magnetic field and the electric field. All EM waves are transverse in nature. They all travel at the speed of light, [math]c = 3.00 \times 10^8 \frac{m}{s}[/math]. That means [math]\lambda \propto \frac{1}{f}[/math], as [math]v = \lambda f[/math] and [math]v = 3.00 \times 10^8 \frac{m}{s}[/math]. The photon energy of a wave is measured in joules and electron volts and can be calculated as follows: [math]e = hf = \frac{ch}{\lambda}[/math] where h = Planck's constant = [math]6.62607 \times 10^{-34} Js[/math]. Radio waves are the waves with the least energy, longest wavelength, and smallest frequency. These can be split up into AM waves, FM waves, short radio waves, telemetry/millimeter-waves, and terahertz waves. Next are microwaves which are used in microwaves to heat food and infrared waves which humans emit. After that are visible light waves which things like lava emit. Ultraviolet rays are next. Then come x-rays and gamma rays which have the highest energies.
  
 
===Spectroscopy===
 
===Spectroscopy===
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Ultraviolet Filter: Block ultraviolet rays but transmit visible light rays, ultraviolet pass and ultraviolet bandpass filters are much less common, used in cameras
 
Ultraviolet Filter: Block ultraviolet rays but transmit visible light rays, ultraviolet pass and ultraviolet bandpass filters are much less common, used in cameras
  
−
Neutral Density Filter: Attenuate all wavelengths of visible light, optical density is the common logarithm of the transmission coefficient, which is <math>amplitude_{initial}:amplitude_{incident}</math> or <math>intensity_{initial}:intensity_{incident}</math>, make photographic exposures longer
+
Neutral Density Filter: Attenuate all wavelengths of visible light, optical density is the common logarithm of the transmission coefficient, which is [math]amplitude_{initial}:amplitude_{incident}[/math] or [math]intensity_{initial}:intensity_{incident}[/math], make photographic exposures longer
  
 
Polarizer Filter: Blocks light depending on its polarization, usually made of Polaroid, sunglasses and photography, darker color
 
Polarizer Filter: Blocks light depending on its polarization, usually made of Polaroid, sunglasses and photography, darker color
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=====Absorption=====
 
=====Absorption=====
  
−
Absorption spectra are the little bits of incident radiation absorbed by the material. They are helpful in chemical analysis of stars (determining what they are made of and what quantity). Here is an example absorption spectra:
+
Absorption spectra are the little bits of incident radiation absorbed by the material. They are helpful in chemical analysis of stars (determining what they are made of and what quantity). [https://commons.wikimedia.org/wiki/File:Spectrum-sRGB.svg Here is an example absorption spectrum.]
−
 
 
−
[[File:https://commons.wikimedia.org/wiki/File:Spectrum-sRGB.svg]]
 
  
 
=====Emission=====
 
=====Emission=====
  
−
Emission spectra are the photons emitted from a material when electrons from the atom are excited (e.g., from being heated). They are helpful in determining the composition of stars. Here is an example emission spectra:
+
Emission spectra are the photons emitted from a material when electrons from the atom are excited (e.g., from being heated). They are helpful in determining the composition of stars. [https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.png Here is an example emission spectrum.]
−
 
 
−
[[File:https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.png]]
 
  
 
===Wave Phenomena===
 
===Wave Phenomena===
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====Doppler Effect====
 
====Doppler Effect====
−
The Doppler Effect is a difference in the frequency of a wave caused by a source moving relative to the observer.  The Doppler Effect occurs because when an object emitting a wave is moving, the crests of the wave will bunch up in front of the object and the crests of the wave will be more spread out behind it.  This causes a higher frequency of a wave when its source moves towards the observer and a lower frequency of a wave when its source moves away from the observer.  An example of this is a siren passing by.  It will sound higher pitched as it approaches, but then sound lower after it passes.  The following equation is used to calculate the frequency of a wave using the Doppler effect:  <math>f=\left (\frac{c+v_r}{c+v_s} \right )f_0</math>.    <math>f</math> is the observed frequency, <math>f_0</math> is the emitted frequency, <math>c</math> is the wave's velocity in the medium, <math>v_r</math> is the velocity of the observer relative to the medium, it is positive when the observer moves towards the source and vice versa, <math>v_s</math> is the velocity of the source relative to the medium, it is positive when the source moves away from the observer and vice versa.
+
The Doppler Effect is a difference in the frequency of a wave caused by a source moving relative to the observer.  The Doppler Effect occurs because when an object emitting a wave is moving, the crests of the wave will bunch up in front of the object and the crests of the wave will be more spread out behind it.  This causes a higher frequency of a wave when its source moves towards the observer and a lower frequency of a wave when its source moves away from the observer.  An example of this is a siren passing by.  It will sound higher pitched as it approaches, but then sound lower after it passes.  The following equation is used to calculate the frequency of a wave using the Doppler effect:  [math]f=\left (\frac{c+v_r}{c+v_s} \right )f_0[/math].    [math]f[/math] is the observed frequency, [math]f_0[/math] is the emitted frequency, [math]c[/math] is the wave's velocity in the medium, [math]v_r[/math] is the velocity of the observer relative to the medium, it is positive when the observer moves towards the source and vice versa, [math]v_s[/math] is the velocity of the source relative to the medium, it is positive when the source moves away from the observer and vice versa.
  
 
[[File:Doppler effect.png|500px]]
 
[[File:Doppler effect.png|500px]]
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The normal, incident ray, and reflected ray all lie on the same plane.
 
The normal, incident ray, and reflected ray all lie on the same plane.
  
−
The incident ray is the same angle from the normal as the reflected ray: <math>\theta_i = \theta_r</math>
+
The incident ray is the same angle from the normal as the reflected ray: [math]\theta_i = \theta_r[/math]
  
 
The incident ray and reflected ray are on opposite sides on the normal.
 
The incident ray and reflected ray are on opposite sides on the normal.
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=====Snell's Law=====
 
=====Snell's Law=====
−
The index of refraction, also called refractive index, is a measure of how light refracts in a medium.  Its formula is <math>n=\frac{c}{v}</math>.  ''n'' is the refractive index, ''c'' is the speed of light in a vacuum, and ''v'' is the speed of light in that medium.
+
The index of refraction, also called refractive index, is a measure of how light refracts in a medium.  Its formula is [math]n=\frac{c}{v}[/math].  ''n'' is the refractive index, ''c'' is the speed of light in a vacuum, and ''v'' is the speed of light in that medium.
  
−
Snell's Law states that the ratio of the velocities of a wave in two media is equal to the ratio of the sine of the angles of incidence, which is also equal to the reciprocal of the ratio of the refractive indices.  The formula is <math>\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}</math>.  <math>\theta</math> is the angle of incidence/reflection, which is measured from the normal, ''v'' is the velocity out of/in the medium, and ''n'' is the refractive index. Angles are measured from the normal.
+
Snell's Law states that the ratio of the velocities of a wave in two media is equal to the ratio of the sine of the angles of incidence, which is also equal to the reciprocal of the ratio of the refractive indices.  The formula is [math]\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}[/math].  [math]\theta[/math] is the angle of incidence/reflection, which is measured from the normal, ''v'' is the velocity out of/in the medium, and ''n'' is the refractive index. Angles are measured from the normal.
  
 
=====Apparent Depth=====
 
=====Apparent Depth=====
−
When refraction occurs, velocity changes and frequency remains the same, so the wavelength of the wave must change because <math>v=\lambda f</math>. In general, the wave is partially reflected and partially refracted. The ratio of real depth to apparent depth is the ratio of the refractive index of water to that of air.
+
When refraction occurs, velocity changes and frequency remains the same, so the wavelength of the wave must change because [math]v=\lambda f[/math]. In general, the wave is partially reflected and partially refracted. The ratio of real depth to apparent depth is the ratio of the refractive index of water to that of air.
  
 
=====Kerr and Pockels Effects=====
 
=====Kerr and Pockels Effects=====
−
The Kerr Effect is the change of refractive index of a material because of an applied electric field. <math>\Delta n \propto E^2</math>, meaning the change in the refractive index is proportional to the square of the energy of the electric field. The Kerr Electro-Optic Effect, or DC Kerr Effect, is when a slow varying electric field is applied. This makes the material birefringent, meaning the material shows different indices of radiation for light polarized parallel and perpendicular to the electric field. The difference is shown by the equation <math>\Delta n = \lambda KE^2</math> where <math>\Delta n</math> is the change in the index of reflection, <math>\lambda</math> is the wavelength of light, K is the Kerr Constant for the material, and E is the energy of the electric field. The Optical Kerr Effect, or AC Kerr Effect, is when the electric field is due to the light itself. The Magneto-Optic Kerr Effect is when light reflected from a magnetized object has a slightly rotated plane of polarization.
+
The Kerr Effect is the change of refractive index of a material because of an applied electric field. [math]\Delta n \propto E^2[/math], meaning the change in the refractive index is proportional to the square of the energy of the electric field. The Kerr Electro-Optic Effect, or DC Kerr Effect, is when a slow varying electric field is applied. This makes the material birefringent, meaning the material shows different indices of radiation for light polarized parallel and perpendicular to the electric field. The difference is shown by the equation [math]\Delta n = \lambda KE^2[/math] where [math]\Delta n[/math] is the change in the index of reflection, [math]\lambda[/math] is the wavelength of light, K is the Kerr Constant for the material, and E is the energy of the electric field. The Optical Kerr Effect, or AC Kerr Effect, is when the electric field is due to the light itself. The Magneto-Optic Kerr Effect is when light reflected from a magnetized object has a slightly rotated plane of polarization.
  
−
The Pockels Effect is the change of refractive index of a crystal that does not show inversion symmetry, such as lithium niobate and gallium arsenide, because of an applied electric field. It differs from the Kerr effect in that <math>\Delta n \propto E</math>, meaning the change in the refractive index is linear instead of quadratic.
+
The Pockels Effect is the change of refractive index of a crystal that does not show inversion symmetry, such as lithium niobate and gallium arsenide, because of an applied electric field. It differs from the Kerr effect in that [math]\Delta n \propto E[/math], meaning the change in the refractive index is linear instead of quadratic.
  
 
=====Refractive Indices=====
 
=====Refractive Indices=====
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| 2.15 - 2.18
 
| 2.15 - 2.18
 
|-
 
|-
−
| Potassium niobate (<math>KNbO_3</math>)
+
| Potassium niobate ([math]KNbO_3[/math])
 
| 2.28
 
| 2.28
 
|-
 
|-
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There are several helpful formulas and equations to know.
 
There are several helpful formulas and equations to know.
 
*Frequency and Period
 
*Frequency and Period
−
**<math>f=1/T</math>
+
**[math]f=1/T[/math]
 
*Rates
 
*Rates
−
**<math>r=d/t</math>
+
**[math]r=d/t[/math]
 
*Velocity
 
*Velocity
−
**<math>v=\lambda f</math>
+
**[math]v=\lambda f[/math]
 
*Snell's Law
 
*Snell's Law
−
**<math>\sin \theta_1 / \sin \theta_2=v_1 / v_2 = n_2 / n_1</math>
+
**[math]\sin \theta_1 / \sin \theta_2=v_1 / v_2 = n_2 / n_1[/math]
 
*Rayleigh criterion
 
*Rayleigh criterion
 
*Young's Equation
 
*Young's Equation
 
*Gratings
 
*Gratings
 
*Harmonics and Resonant Frequency
 
*Harmonics and Resonant Frequency
−
**<math>f_n = (n + 1) * f_0</math>
+
**[math]f_n = (n + 1) * f_0[/math]
 
*Polarization
 
*Polarization
 
*Brewster's Angle
 
*Brewster's Angle
 
*Energy of a Photon
 
*Energy of a Photon
−
**<math>e=hf=ch/\lambda</math>
+
**[math]e=hf=ch/\lambda[/math]
 
*Dimensional Analysis
 
*Dimensional Analysis
 
*Wavelength of Colors
 
*Wavelength of Colors

Revision as of 06:53, 18 February 2017

Template:EventLinksBox

In Crave the Wave, participants will demonstrate knowledge and process skills needed to solve problems and answer questions regarding all types and areas of waves and wave motion. A calculator is required for this event.

Regionals Topics

General Wave characteristics
Wave Types
Wave Phenomena
Electromagnetic Waves Insert info on: energy carried (AM/FM only), standard wavelength bands, their uses and dangers, how the electromagnetic spectrum relates to everyday life, and mechanical and electromagnetic waves.
Spectroscopy: Filters and Primary colors

Some calculations are required, such as calculation of frequency, period, wavelength, and speed.

Wave Characteristics

Types of Waves

The two main types of waves are longitudinal (An example of this could be a P-wave) and transverse (An example of this could be a S-wave). Transverse waves propagate perpendicular to the direction of the wave. Longitudinal waves move parallel to the direction of the wave. These two wave types can be modeled with a Slinky. Start by having two people stretch a Slinky. To model a transverse wave, have one person shake their end of the Slinky with an up-and-down or a right-to-left motion. To model a longitudinal wave, keep the Slinky completely straight and have one person quickly push their end of the Slinky to the other person. S-wave animation.gifP-wave animation.gif

Other types of waves include surface waves and torsional waves. Surface waves are waves that travel along the boundary of two media. The particles in a surface wave move in a circular motion. Torsional waves twist and spin. It is like a screw being drilled, or moving your arms back and forth while keeping them flat.

Transverse Waves

The main parts of a transverse wave are the crest, trough, wavelength, and amplitude. Also, there are additional characteristics of waves, such as frequency and period.

  • Crest- the highest point of a wave. Also called peak.
  • Trough- the lowest point of a wave.
  • Rest position- the position the wave would be in if there were no disturbances along it. Also called normal position and equilibrium position.
  • Wavelength- the distance between two crests or troughs. Measured by distance units of the metric system.
  • Amplitude- the distance between a crest or trough and the rest position. Measured by distance units of the metric system.
  • Frequency- the number of wavelengths passed per second. Measured in Hertz (Hz).
  • Period- the time a wave takes to complete a wavelength. Measured in seconds.
  • Direction of Motion- the direction in which the wave moves
  • Direction of Oscillation- the direction in which particles in the wave move, perpendicular to the direction of motion
  • Velocity- the speed and direction in which the wave is moving, equal to wavelength times frequency

Some of these parts are shown in the picture below:Waves wavelength.jpg

Longitudinal Waves
  • Compression- the most compressed point of a wave
  • Rarefaction- the least compressed point of a wave
  • Rest Position- the position the wave would be in if there were no disturbances along it. Also called normal position and equilibrium position.
  • Wavelength- distance between two compressions or rarefactions. Measured by distance units of the metric system.
  • Frequency- the number of wavelengths passed per second. Measured in Hertz (Hz).
  • Period- the time a wave takes to complete a wavelength. Measured in seconds.
  • Direction of Motion- the direction in which the wave moves
  • Direction of Oscillation- the direction in which particles in the wave move, parallel to the direction of motion
  • Velocity- the speed and direction in which the wave is moving, equal to wavelength times frequency
Surface Waves
  • Crest- the highest point of a wave. Also called peak.
  • Trough- the lowest point of a wave
  • Rest Position- the position the wave would be in if there were no disturbances along it. Also called normal position, equilibrium position, and still-water position
  • Wavelength- distance between two crests or troughs. Measured by distance units of the metric system.
  • Frequency- the number of wavelengths passed per second. Measured in Hertz (Hz).
  • Period- the time a wave takes to complete a wavelength. Measured in seconds.
  • Direction of Motion- the direction in which the wave moves
  • Direction of Oscillation- the direction in which particles in the wave move, circular motion
  • Wave Height- the vertical distance between a crest and a trough
  • Velocity- the speed and direction in which the wave is moving, equal to wavelength times frequency
Torsional Waves
  • Direction of Motion- the direction in which the wave moves
  • Velocity- the speed and direction in which the wave is moving
  • Direction of Oscillation- the direction in which particles of the wave move

Electromagnetic Spectrum

1280px-EM Spectrum Properties edit svg.png Untitled1.png The electromagnetic field is a combination of the magnetic field and the electric field. All EM waves are transverse in nature. They all travel at the speed of light, [math]c = 3.00 \times 10^8 \frac{m}{s}[/math]. That means [math]\lambda \propto \frac{1}{f}[/math], as [math]v = \lambda f[/math] and [math]v = 3.00 \times 10^8 \frac{m}{s}[/math]. The photon energy of a wave is measured in joules and electron volts and can be calculated as follows: [math]e = hf = \frac{ch}{\lambda}[/math] where h = Planck's constant = [math]6.62607 \times 10^{-34} Js[/math]. Radio waves are the waves with the least energy, longest wavelength, and smallest frequency. These can be split up into AM waves, FM waves, short radio waves, telemetry/millimeter-waves, and terahertz waves. Next are microwaves which are used in microwaves to heat food and infrared waves which humans emit. After that are visible light waves which things like lava emit. Ultraviolet rays are next. Then come x-rays and gamma rays which have the highest energies.

Spectroscopy

Colors

Colors.png The primary colors of light are red, green, and blue, and the secondary colors of light are yellow, cyan, and magenta. Conversely, the primary colors of pigments are yellow, cyan, and magenta, and the secondary colors of pigments are red, green, and blue.

Filters

Filters: absorptive and dichroic/interference/thin film/reflective

Absorptive filters are usually made of glass with several compounds added which absorb specific wavelengths of light. They can also be made of plastic, which the compounds are added to, to produce gel filters.

Dichroic filters have little reflective cavities which resonate with specific wavelengths. Using destructive interference, the wavelengths are canceled out, leaving the rest of the wavelengths to pass through. They are used for precise scientific work since their exact color range can be controlled. Interference filters are more expensive and more delicate.

Long-Pass Filter: Transmits waves with wavelengths longer than a specific range, Attenuates waves with shorter wavelengths

Short-Pass Filter: Transmits waves with wavelengths shorter than a specific range, Attenuates waves with longer wavelengths

Bandpass-Filter: Combination of long-pass and short-pass filters, transmits waves with a wavelength in a specific interval

Monochromatic Filter: Only a small range (usually one color) of wavelengths is allowed to pass.

Infrared Filter: The term can refer to infrared-passing or infrared cut-off filters, infrared photography (passing), projectors (cut-off),

Ultraviolet Filter: Block ultraviolet rays but transmit visible light rays, ultraviolet pass and ultraviolet bandpass filters are much less common, used in cameras

Neutral Density Filter: Attenuate all wavelengths of visible light, optical density is the common logarithm of the transmission coefficient, which is [math]amplitude_{initial}:amplitude_{incident}[/math] or [math]intensity_{initial}:intensity_{incident}[/math], make photographic exposures longer

Polarizer Filter: Blocks light depending on its polarization, usually made of Polaroid, sunglasses and photography, darker color

Spectra

Absorption

Absorption spectra are the little bits of incident radiation absorbed by the material. They are helpful in chemical analysis of stars (determining what they are made of and what quantity). Here is an example absorption spectrum.

Emission

Emission spectra are the photons emitted from a material when electrons from the atom are excited (e.g., from being heated). They are helpful in determining the composition of stars. Here is an example emission spectrum.

Wave Phenomena

Interference

Two waves strike each other.

Constructive

Constructive Interference.png The two waves reinforce each other.

Destructive

Destructive Interference.png The two waves cancel out each other.

Doppler Effect

The Doppler Effect is a difference in the frequency of a wave caused by a source moving relative to the observer. The Doppler Effect occurs because when an object emitting a wave is moving, the crests of the wave will bunch up in front of the object and the crests of the wave will be more spread out behind it. This causes a higher frequency of a wave when its source moves towards the observer and a lower frequency of a wave when its source moves away from the observer. An example of this is a siren passing by. It will sound higher pitched as it approaches, but then sound lower after it passes. The following equation is used to calculate the frequency of a wave using the Doppler effect: [math]f=\left (\frac{c+v_r}{c+v_s} \right )f_0[/math]. [math]f[/math] is the observed frequency, [math]f_0[/math] is the emitted frequency, [math]c[/math] is the wave's velocity in the medium, [math]v_r[/math] is the velocity of the observer relative to the medium, it is positive when the observer moves towards the source and vice versa, [math]v_s[/math] is the velocity of the source relative to the medium, it is positive when the source moves away from the observer and vice versa.

Doppler effect.png

Standing Waves

Standing waves.gif Standing waves are when a wave does not appear to be made up of moving waves. This is from a combination of reflection and interference. Nodes are points of maximum destructive interference while anti-nodes are points of maximum constructive interference.

The animation below shows the standing wave in pink, the initial wave in yellow, and the reflected beam in cyan (dotted):Standing wave.gif

Reflection

The change of direction so that the wave bounces off into the same medium in which it originated.

Specular

If the reflection interface is very smooth, specular reflection will occur. Specular reflection is mirror-like (forms images).

Laws of reflection:

The normal, incident ray, and reflected ray all lie on the same plane.

The incident ray is the same angle from the normal as the reflected ray: [math]\theta_i = \theta_r[/math]

The incident ray and reflected ray are on opposite sides on the normal.

An image in a glass mirror is 1)virtual, 2)reversed, 3)the right side up, 4)the same size of the object, and 5)the same distance behind the mirror as the object is in front of the mirror.

Diffuse

If the reflection interface is rough (non-metallic), diffuse reflection will occur. Diffuse reflection is where an incident ray is reflected at many different angles as opposed to specular reflection with only one angle of reflection. The visibility of objects is primarily due to diffuse reflection. Diffuse interreflection occurs when light reflected off a nearby object reflects off surrounding objects, illuminating them.

Refraction

Refraction is the change in direction of a wave caused by a change in its medium. Refraction is responsible for rainbows and mirages.

Snell's Law

The index of refraction, also called refractive index, is a measure of how light refracts in a medium. Its formula is [math]n=\frac{c}{v}[/math]. n is the refractive index, c is the speed of light in a vacuum, and v is the speed of light in that medium.

Snell's Law states that the ratio of the velocities of a wave in two media is equal to the ratio of the sine of the angles of incidence, which is also equal to the reciprocal of the ratio of the refractive indices. The formula is [math]\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}[/math]. [math]\theta[/math] is the angle of incidence/reflection, which is measured from the normal, v is the velocity out of/in the medium, and n is the refractive index. Angles are measured from the normal.

Apparent Depth

When refraction occurs, velocity changes and frequency remains the same, so the wavelength of the wave must change because [math]v=\lambda f[/math]. In general, the wave is partially reflected and partially refracted. The ratio of real depth to apparent depth is the ratio of the refractive index of water to that of air.

Kerr and Pockels Effects

The Kerr Effect is the change of refractive index of a material because of an applied electric field. [math]\Delta n \propto E^2[/math], meaning the change in the refractive index is proportional to the square of the energy of the electric field. The Kerr Electro-Optic Effect, or DC Kerr Effect, is when a slow varying electric field is applied. This makes the material birefringent, meaning the material shows different indices of radiation for light polarized parallel and perpendicular to the electric field. The difference is shown by the equation [math]\Delta n = \lambda KE^2[/math] where [math]\Delta n[/math] is the change in the index of reflection, [math]\lambda[/math] is the wavelength of light, K is the Kerr Constant for the material, and E is the energy of the electric field. The Optical Kerr Effect, or AC Kerr Effect, is when the electric field is due to the light itself. The Magneto-Optic Kerr Effect is when light reflected from a magnetized object has a slightly rotated plane of polarization.

The Pockels Effect is the change of refractive index of a crystal that does not show inversion symmetry, such as lithium niobate and gallium arsenide, because of an applied electric field. It differs from the Kerr effect in that [math]\Delta n \propto E[/math], meaning the change in the refractive index is linear instead of quadratic.

Refractive Indices
Material Refractive Index
Vacuum 1
Gases at 0°C and 1 atm
Air 1.000293
Carbon Dioxide 1.00045
Helium 1.000036
Hydrogen 1.000132
Liquids at 20°C
Arsenic Trisulfide and Sulfur in Methylene Iodide 1.9
Benzene 1.501
Carbon Disulfide 1.628
Carbon Trichloride 1.461
Ethyl Alcohol (Ethanol) 1.361
Silicone Oil 1.336-1.582
Water 1.3330
10% Glucose Solution in Water 1.3477
20% Glucose Solution in Water 1.3635
60% Glucose Solution in Water 1.4394
Solids at Room Temperature
Titanium Dioxide (Rutile Phase) 2.614
Diamond 2.419
Strontium Titanate 2.41
Amber 1.55
Fused Silica (Fused Quartz) 1.458
Sodium Chloride 1.544
Other
Liquid Helium 1.025
Water Ice 1.31
Cornea (human) 1.373-1.401
Lens (human) 1.386-1.406
Acetone 1.36
Ethanol 1.36
Glycerol 1.4729
Bromine 1.661
Teflon AF 1.315
Teflon 1.35-1.38
Cytop 1.34
Sylgard 184 (Polydimethylsiloxane) 1.4118
Polylactic acid 1.46
Acrylic glass 1.490 - 1.492
Polycarbonate 1.584 - 1.586
PMMA 1.4893 - 1.4899
PETg 1.57
PET 1.5750
Kerosene 1.39
Crown glass (pure) 1.50 - 1.54
Flint glass (pure) 1.60 - 1.62
Crown glass (impure) 1.485 - 1.755
Flint glass (impure) 1.523 - 1.925
Pyrex (a borosilicate glass) 1.470
Cryolite 1.338
Rock salt 1.516
Sapphire 1.762–1.778
Sugar Solution, 25% 1.3723
Sugar Solution, 50% 1.4200
Cubic zirconia 2.15 - 2.18
Potassium niobate ([math]KNbO_3[/math]) 2.28
Silicon carbide 2.65 - 2.69
Cinnabar (Mercury sulfide) 3.02
Gallium(III) phosphide 3.5
Gallium(III) arsenide 3.927
Zinc Oxide 2.4
Germanium 4.05 - 4.01
Silicon 3.48 - 3.42

Diffraction

Diffraction.gif

Diffraction is when a wave spreads out when encountering a corner or hole, such as a doorway or slit, that is comparable to its wavelength. Francesco Maria Grimaldi, and Italian scientist, coined the word 'diffraction.' Diffraction is described by the Huygens-Fresnel Principle.

State Topics

At States you will also need to demonstrate your knowledge about seismic waves.

Seismic Waves

There are 5 major earthquake waves:

  • P-waves- aka primary waves, are longitudinal waves. They are the first to arrive. They can travel through liquids.
  • S-waves- aka secondary or shear waves, are transverse waves. They are second to arrive. They cannot travel through liquids.
  • Surface Waves- combinations of P and S waves and occur on the surface. They are the slowest waves.
    • Rayleigh Waves- waves that roll in an ocean-like motion.
    • Love Waves- waves that move in side to side, horizontally. Love waves cause the most damage.

P-wave medium.jpg S-wave medium.jpg Love medium.jpg Rayleigh medium.jpg L wave resized.gif R wave resized.gif

National Topics

In addition to the Regional and State topics, Nationals will introduce Breaking ocean waves and Tsunamis.

Breaking Ocean Waves

Tsunamis

A tsunami, or seismic sea wave, is a series of ocean waves that can be caused by things such as earthquakes or volcanic activity.

Notable Tsunamis

The earthquake and tsunami in the Indian Ocean on December 26, 2004, was the most devastating tsunami ever recorded. The estimated amount of casualties was 280,000 people.

Japan has a history of tsunamis, but a recent one was the earthquake of the coast of Japan on March 11, 2011. The tsunami is probably most known for the three nuclear reactors at the Fukushima plant that had meltdowns, causing the meltdown to be declared the largest nuclear disaster since Chernobyl.

Equations to Know

There are several helpful formulas and equations to know.

  • Frequency and Period
    • [math]f=1/T[/math]
  • Rates
    • [math]r=d/t[/math]
  • Velocity
    • [math]v=\lambda f[/math]
  • Snell's Law
    • [math]\sin \theta_1 / \sin \theta_2=v_1 / v_2 = n_2 / n_1[/math]
  • Rayleigh criterion
  • Young's Equation
  • Gratings
  • Harmonics and Resonant Frequency
    • [math]f_n = (n + 1) * f_0[/math]
  • Polarization
  • Brewster's Angle
  • Energy of a Photon
    • [math]e=hf=ch/\lambda[/math]
  • Dimensional Analysis
  • Wavelength of Colors

Sample Questions

If the frequency of a light wave is 2 Hz (2 cycles per second), what is the wavelength?
If the wavelength of a sound wave through air at 20 degrees Celsius is 2 cm, what is the frequency in Hz (cycles per second)?
If the period is 2 seconds, what is the Frequency?
What is Destructive Interference?
Which seismic wave is faster? Primary waves or Secondary waves?
Given an image of a wave, identify the wavelength.

Sample Exercises

Crave the Wave State Test (2008)
Crave the Wave Test (2009)

Websites and Resources

A Crave the Wave Resource Binder (2007-2008)
Introduction to Waves
Sound Waves
Light and Color
Reflection and the Ray Model of Light
Refraction and the Ray Model of Light
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