A sound wave isn't a physical thing traveling through the room — it's a pattern traveling through the air. A vibrating object (a guitar string, a speaker cone, your vocal cords) pushes on the air molecules next to it. Those molecules bump into their neighbors, which bump into their neighbors, and so on — the disturbance hands itself forward through the medium.
The distance of one full repeating pattern. Measured in meters.
How many full patterns repeat per second. Measured in hertz (Hz).
Period (T) is the flip side of frequency — how long a single repeat takes.
In one period T, a wave moves forward exactly one wavelength λ. Speed is distance over time, so:
For sound in air at room temperature, v stays close to 343 m/s no matter what note is playing. That means frequency and wavelength are locked in a trade-off — push one up, the other has to come down to keep their product constant.
A tuning fork vibrates at 440 Hz (the musical note A). Find its wavelength in air.
Not all waves vibrate the same way relative to the direction they travel.
Vibration is perpendicular to travel direction. A wave on a rope shaken up and down, or a ripple on water.
Vibration is parallel to travel direction — a push-pull along the same line. This is what sound actually is.
Since compressions and rarefactions are hard to draw as a push-pull pattern, we almost always graph sound as pressure (or displacement) versus position — which produces a wavy, transverse-LOOKING curve, even though the underlying motion is longitudinal.
Same wave, two pictures. The top graph is how we usually draw a wave — height vs. position. The bottom row is what the air molecules are ACTUALLY doing — squeezing together and spreading apart along the same line the wave travels.
Raise the frequency and watch the wavelength shrink — speed stays fixed, so the two must trade off. In the bottom row, look for where the dots bunch together (compression) and where they spread apart (rarefaction).
You now have the vocabulary to describe any wave precisely. Lesson 3-1-2 connects these numbers to what you actually perceive: frequency becomes pitch, and amplitude (a number we haven't used yet — how big the pressure swing is) becomes loudness.