A wave is a disturbance that carries energy from one place to another. A transverse wave (crest, trough, amplitude and wavelength) will move particles at right angles to its direction of travel, a longitudinal wave (compression, rarefraction and wavelength) will move particles in the direction of travel, however, the particles will only oscillate, or "wave" back and forth as the energy passes. They will not travel with the wave, instead they will return to their initial location. Transverse waves do not need a medium to travel in (think radio waves, infrared or visible light), but longitudinal waves (sound waves or earthquake waves) transmit by the particles bumping into other particles and "transmitting" by collisions.
The speed of some waves can depend on the material the wave travels through (though electromagnetic waves travel at the speed of light), the amount of energy each wave carries determines its amplitude and the frequency of the wave is inversely proportional to its period. Waves that meet traveling in opposite directions can create what is called constructive interference (which can lead to resonance) or destructive interference. The musical theories of consonance and dissonance are built off the idea that two frequencies can match up in a way to please you or make you cringe.
Intensity is the idea that a unit of power per unit area is what you would term loudness. You can think of it in the sense that you are delivering a certain amount of energy to an area. More discussion should be had between the idea of "head phones" and "ear buds" and instensity vs volume.
The doppler effect is a phenomenon that is used all over the world (and universe) for many things wave. Its most important application is its help in discovering that the universe is expanding, however, in terms of sound it is the understanding that as you move toward an object emitting sound (or as it moves toward you) the sound waves are crunched together changing the percieved "pitch" (the frequency) of the sound. Similarly, as the object (or you) move away, the pitch would appear to drop below its actual frequency.
In harmonics, a standing wave (a wave that stays in place because it is bound) will vibrate and create an opportunity to constructively interfere with itself (in the right conditions it can resonate). The first or lowest frequency achieved is called the fundamental frequency), On a stringed instrument its takes at least 1/2 of a wavelength, but then harmonics can be achieved on every half or whole from there. On a wind instrument that is closed at one end the first harmonic is located on 1/4 a wavelength, but then repeats each half wavelength from there. On a wind instrument that is open at both ends the first harmonic is located at 1/2 a wavelength and then achieved at each half and whole from there.