Physics uses basic models to simplify complex systems. A common model is the particle. Particles are point-like objects with no internal structure, just properties like mass and velocity. More complicated properties like rotation, and friction are often ignored. We've used the particle model to understand phenomena like: momentum, gravitation, Coulomb's law,and current
The model of a particle can be applied to things like electrons, gases, or stars.

Another commonly used model is the wave. Waves are different from the particle model in some interesting ways. They don't exist at a point. They spread out in every direction at a constant speed. They have zero mass, and they can overlap with each other without interacting.

A wave is produced when a medium is disrupted. The wave is the disruption spreading through the medium.

The nature of each medium gives waves different properties. If you throw a pebble into a pond you see a wave spread out along the surface of the water. When a tree falls in the forest you can hear the sound waves spread out through the air. When you look at the sky you see electro-magnetic waves made by stars.

Media and Wave Speed

When a wave propagates, what is moving is energy, not matter. The speed of propagation is determined by the medium. Properties like frequency, amplitude, or wavelength generally don't affect the speed.

Each type of wave has a different mechanism of propagation. The speed and possibility of a wave propagating through a medium is different for each wave type.

Sound travels faster in dense media because the atoms are closer together. This means the atoms don't have to move as far to collide.

A light wave is slower in dense media because as the light wave propagates through a medium it produces ripples that interfere in a way that slows the group velocity of the light wave.

How Waves Propagates ?

Propagate is the word we use to describe waves moving. We try not to say move, because waves are a disturbance transmitting through the medium. The medium doesn't move. Each medium has their own mechanism of propagation, but they share some common principles.

Each medium has their own mechanism of propagation, but there are some general principles.

A medium at rest is in equilibrium; the forces are in balance. A disruption spreads through a medium bringing it out of equilibrium.

Sound waves are vibrations that propagate through matter. They are produced by changes in pressure and velocity. Your ear senses the amplitude and frequency of the vibrations.

A disturbance that produces one or only a few waves is called a pulse.

Waves don't transmit matter, just energy. In the simulation above one particle is highlighted. Watch how it oscillates when it becomes part of the wave, but over time it stays in the same area. Sound waves oscillate parallel to propagation, but most waves oscillate perpendicular to propagation.

Longitudinal Wave = The medium oscillates parallel to the direction of wave propagation.
Examples: sound, slinky

Transverse Wave = The medium oscillates perpendicular to the direction of wave propagation.
Examples: light, string, slinky, sound (in solids), gravity

Click to Run

Periodic Waves

Waves that repeat are called periodic. Periodic waves have these measurable properties.

Period, T = time for one complete wave cycle to pass a point [s]
Frequency, f = number of cycles that pass per second [Hz, 1/s]
Wavelength, λ = distance over which a wave's shape repeats [m]

Waves can have different shapes. The waveform below is a sine square triangle sawtooth wave.

The spectrum of light extends far beyond the visible light that our eyes evolved to detect. Cell phones and Wi-Fi use microwave light to transmit digital information. CT scans use x-ray light to look inside a person's body. Thermometers use infrared light to read temperature. All of these different types of light are produced in the same way.

Changes in an electric and magnetic field don't happen immediately. It takes time for changes in an electromagnetic field to propagate through space. The speed of these changes to the E-M field is the speed of light.

The below simulation shows a charge particle that follow your mause. the white line shows the electric field from a charged particle, the ripples in thr field lines are light

Click to Run

Source code here

A quick acceleration makes high frequency light. Slow acceleration makes low frequency light. You can't quite make a "sonic boom" with light because a charged particle can't move faster than the speed that light waves propagate.

The Speed of Light

In 1676 Ole Rømer estimated that light has a speed by timing the eclipses of Io, one of Jupiter's moons. He found the speed to be around 220 000 000 m/s. This isn't too far from the value we use today.

We can use the speed of light as the velocity in the wave equation.

The speed of light in a vacuum is the fastest possible speed! No object has ever been recorded moving faster. As objects approach the speed of light their time dilates and length contracts.

The Electromagnetic Spectrum

Light can be viewed as a spectrum. The lowest energy, lowest frequency, and longest wavelength are on one end. The highest energy, highest frequency, and shortest wavelength are on the other.

The electromagnetic spectrum is very loosely divided in these regions based on the source of that light.

Microwave and radio waves are produced by changing electric current. Infrared light is mostly produced by the thermal radiation of bodies at room temperature. Visible light comes from thermal radiation (sunlight), chemical reactions (fire), and numerous technologies (LED, laser, cathode ray tube, gas discharge lamps).

Ultraviolet light comes from the same sources as visible light, but at a slightly higher frequency that humans can't see. X-rays can be produced by accelerating electrons very quickly, like in cathode ray vacuum tubes. Gamma rays are similar to X-rays, but they are generally distinguished by coming from radioactive decay instead of electron acceleration.

Some classify microwaves as a subregion inside radio. Also, the x-ray and gamma-ray regions are starting to blend as the technology that produces x-rays improves.

Color Vision

Our eyes have two types of cells that respond to visible light, rods and cones. Rods detect visible light with a high sensitivity. Cones specialize in detecting the wavelength of the light. Cone cells come in different types that are sensitive to different wavelengths of visible light.

The number of colors receptors has varied as life has evolved. Most birds and reptiles have 4 different color receptors. Mammals have 2 color vision, with the exception of primates that have 3 color vision.

Humans are primates, so we mostly have 3 different color receptors, but some color blind humans have 2. They don't see in black and white, they just have trouble telling the difference between some colors, like

Human cones cells respond to 3 overlapping regions on the electromagnetic spectrum. We can see every color on the rainbow from this information.

What about colors not on the rainbow? If multiple cones are activated our brains invent colors to describe the experience, like pink or white.

Click to Run

Information from our eyes is processed in our brains to build a guess about what we are seeing. Our brain's interpretation isn't perfect. We call these mistakes optical illusions.

Thermal Radiation

The particles in all substances move and vibrate in a seemingly random way. Temperature is a measure of the average kinetic energy of these particles. When the temperature is high there is more motion.

When charged particles accelerate they produce light. This means that as substances get hotter they make brighter and higher frequency light.

Click to Run