Distinguish transverse waves (particle motion perpendicular to the wave direction) from longitudinal waves (particle motion parallel to the wave direction), and classify examples such as light, water, and sound waves (MA STE Introductory Physics, Waves, HS-PS4-1).

What this topic is asking

Waves come in two basic types, and the Massachusetts Introductory Physics MCAS expects you to tell them apart by how the medium moves. You must distinguish a transverse wave (the medium moves perpendicular to the wave's direction) from a longitudinal wave (the medium moves parallel to the wave's direction), and classify common examples: light and water waves as transverse, sound waves as longitudinal. The crosscutting idea is structure and function: the way the particles move sets how the wave looks and behaves.

Transverse waves

Picture shaking the end of a long rope up and down: the wave races along the rope (horizontally), but each bit of rope only moves up and down (vertically), at right angles to the travel direction. That perpendicular motion is the signature of a transverse wave. Transverse waves include:

• Waves on a string or rope.
• Water waves (to a good approximation, the surface moves up and down as the wave moves across).
• All electromagnetic waves, including visible light, radio, and X-rays, treated in the electromagnetic spectrum topic.

On a transverse wave, the wavelength is measured crest to crest, and the amplitude is the height of a crest above the rest position.

Longitudinal waves

Think of pushing and pulling the end of a stretched spring (a "slinky") along its length: a pulse of squashed-together coils travels along the spring in the same direction you push. The coils move back and forth along the spring, not across it. Sound is the most important longitudinal wave the MCAS tests: a speaker pushes air molecules back and forth, sending compressions and rarefactions outward. On a longitudinal wave, one wavelength runs from one compression to the next, and a bigger amplitude means the compressions are denser (a louder sound).

Both move energy, not matter

It is easy to think material moves with a wave because the pattern clearly travels, but it does not. In a transverse water wave, a floating object bobs up and down in place. In a longitudinal sound wave, each air molecule jiggles back and forth around its average spot while the sound energy passes through. Keeping this straight prevents a common error: confusing the motion of the wave with the motion of the medium.

Worked example

Reference-sheet note

The reference sheet gives the wave equation $v = f\lambda$, which applies to both wave types, but it does not list the wave types themselves. What you recall is the perpendicular-versus-parallel distinction, the features of each type (crest and trough for transverse, compression and rarefaction for longitudinal), the standard examples (light and water transverse, sound longitudinal), and that both move energy without moving matter.

Try this

Q1. State whether a water wave is transverse or longitudinal, and name its high and low points. [2]

• Cue. Transverse; the high points are crests and the low points are troughs.

Q2. Name the two regions of a longitudinal wave and give one example of such a wave. [2]

• Cue. Compressions and rarefactions; sound is an example.