Waves Terms
Amplitude
Amplitude has different physical meanings across different types of waves, but mathematically it's always the same. In the basic solution to simple oscillation, x(t) = Acos(ω t + φ), the variable A represents the wave's peak amplitude—the largest value x can ever have. This could be the height of the ocean swell, or the voltage coming out of the AC socket in your wall, or the volume of your guitar. (If you live next to a garage band, you know that guitar volume has a much larger amplitude when the guitar is plugged into an amp.)Constructive And Destructive Interference
Overlapping waves can add to each others' amplitudes (constructive interference) or subtract from them (destructive interference). The amount of interference is dependent on each wave's amplitude, but also strongly influenced by the phase of the waves. Build it up, tear it down.Cycle
The chunk of motion that's repeated in wave motion is called a cycle—it's the root of the wave's pattern. Cycles are also spotted under Tour de France enthusiasts.The Doppler Effect
As you watch a moving object pass you, the freqeuncy of the sound it's making changes. This is an example of the Doppler Effect, which is true for all waves made by moving objects—sound, light, and so on. It's Doppler that's responsible for the WEEEEEEE-OOOOOOOO noises you hear at NASCAR races.Frequency
Frequency is the number of complete oscillations per second made by a wave, measured in hertz (1 Hz = 1 s-1). In the basic solution to simple oscillation, x(t) = Acos(ωt + φ), the variable ω represents a wave's angular frequency, which is measured in rad/s. Angular frequency can be converted to frequency by dividing by 2π (the number of radians in one cycle):
. Frequency—normal frequency, not angular frequency—is the inverse of the period of the wave: 
. The frequency of a wave is also inversely related to the wave's wavelength: 
. Higher frequency light has more energy than lower frequency light, and looks more blue than red. Higher frequency sound is higher in pitch than lower frequency sound. Higher frequency flyer miles can get you a better seat on selected domestic flights.Longitudinal Wave
In a longitudinal wave, the direction of oscillation is the same as the direction of propagation. The most common example is sound, where air molecules compress and expand as the noise moves from a teacher's vocal cords through the air of the classroom to your ear.Nodes And Antinodes
In a standing wave, there are points on the wave that never move—these are the nodes of the wave. The points that move the most, usually halfway between the nodes, are called antinodes. Nodes have no movement; antinodes are anti-everything and want to move as far away as possible.Oscillation
Many times, wave or wave-like motion is referred to as oscillation (sometimes also called "periodic motion"). Oscillations are repetitive motions of a value away from and back to its equilibrium point, such as a block suspended on a spring or the pendulum on a grandfather clock. The block and the pendulum both have an equilibrium point they want to rest at, but repeatedly move away from it, back and forth, over and over. Oscillation is not restricted to physical things—the electricity in your wall is a wave that oscillates between +120√2 V and -120√2 V. This up-and-down / back-and-forth / side-to-side motion is usually described by wave equations. It's the same slang surfers use when they talk about the gnarly oscillations they've been catching.Period
Period is the time it takes a wave to complete one full oscillation, measured in seconds. It is the inverse of the frequency of the wave:
. Short period motion happens quickly, like a vibrating electric toothbrush. Long period motion lasts longer, like a rolling ocean swell. Seventh-period French lasts forever.Phase
In the basic solution to simple oscillation, x(t) = Acos(ωt + φ)$, the variable φ is the wave's phase. This represents where in the sine cycle the wave is at time t—while sine normally starts at zero at time zero, it can be shifted left or right by φ. Waves can be in phase with one another if their φ values are equal (or a multiple of one another) or out of phase if their φs don't match up. Phase is usually expressed in degrees or radians, and can be set to stun or kill.Simple Harmonic Motion
The simplest form of oscillation, simple harmonic motion—SHM for the acronym lovers in the audience—happens when the force that pulls an object back to its equilibrium point is proportional to the distance that object is away from its equilibrium point, such as a mass on a spring (Hooke's Law: F = -kx). SHM is simple, it's motion, and it can be sung by most barbershop quartets.Standing Wave
A wave that oscillates but doesn't propagate is called a standing wave, since it appears to be standing still. A guitar string, pinched on both ends, forms a standing wave when it's strummed.Transverse Wave
In a transverse wave, the direction of oscillation is perpendicular to the direction of propagation. Light is a transverse wave, wiggling along its path of motion like a snake.Troughs And Crests
Troughs and crests are the lowest and highest points, respectively, of a wave. A trough is the very bottom of the sine shape (that looks like it would hold slop for hogs), while a crest is the very top of the sine wave (that looks like you could surf on it).Wave
A wave is an oscillation. But more than that, a wave is a repeated set of oscillations—repeated motion away from and back to an equilibrium point. Many kinds of "repetitive motion" can be described as waves, from things we traditionally call waves (light or sound or the motion of the ocean) to back-and-forth motion of physical objects (swing sets or see-saws or clock pendulums). Mechanical waves travel through a medium: sound is a wave of air molecules jostling back and forth, and earthquakes are oscillations in the rock of earth's crust. Electromagnetic waves don't need a medium to travel through—we send radio waves to space to communicate to satellites. "The Wave" travels through a very specific medium: sports stadiums full of people.Wavelength
When a wave like a sine or cosine is graphed, wavelength represents the length on the x-axis between crests (or troughs), measured in meters. Wavelength is the length it takes for the wave to repeat itself. The wavelength of a wave is inversely related to a wave's frequency:
. Longer wavelength light looks more red than blue; longer wavelength sound is lower in pitch. Wavelength is the length it takes for the wave to repeat itself.