Every wave makes the medium move, but not always in the same direction. Shake a rope up and down and the wiggle runs along it. Push and pull the end of a long spring and a squeeze runs along it. Those are the two basic kinds of waves.
Key idea
In a transverse wave, the medium moves across (perpendicular to) the direction the wave travels: crests and troughs. In a longitudinal wave, the medium moves back and forth along the direction the wave travels: compressions (squeezed) and rarefactions (spread out). Sound is longitudinal.
Why it works
A loudspeaker cone pushes forward, squeezing the air in front of it, then pulls back, leaving the air spread out. Those squeezes and stretches travel outward, while each bit of air just jiggles back and forth along the wave's path. The distance from one compression to the next is the wavelength, just as crest to crest is for a transverse wave.
Worked example: Classify the wave
A stadium crowd does "the wave": each person stands up and sits down as the wave sweeps around the stadium. Which kind of wave is it?
- Each person moves up and down.
- The wave travels sideways around the stadium.
- Motion across the direction of travel: transverse.
Answer: Transverse
Worked example: Wavelength of sound
In a sound wave, the compressions are 1.2 m apart. What is the wavelength?
- One compression to the next is one full wave.
- So $\lambda = 1.2$ m. (Compression to the next rarefaction would be only half a wave.)
Answer: 1.2 m
Common mistake
Thinking every wave is transverse, like the picture of a water wave, and being unable to picture sound. Sound has no crests in the air; it is a train of squeezes and stretches moving outward. (Water waves are actually a mix: the water at the surface moves in small circles.)
Earthquakes send both kinds. Longitudinal P waves travel fastest and arrive first; transverse S waves arrive later and cannot cross Earth's liquid outer core, which is one of the ways scientists learned the outer core is liquid.