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How high can it go? A trig function's amplitude is the vertical distance between the midline and the maximum value.
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.
The thing that repeats in a periodic function.
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.
the number of times an event occurs; Jim asked Danielle out with uncommon frequency
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.
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.
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.
A period is a horizontal row of the periodic table.
A sample of matter that is uniform throughout both in its chemical composition and in its physical state.
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.
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.
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 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).
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 refers to the distance between the peaks of two waves.