13.2 Transverse and Longitudinal Waves

A wave is transverse when the medium's particle displacement is perpendicular to the direction of energy transfer. A string wave is the standard mechanical example. If the disturbance travels right, particles oscillate up and down around their equilibrium lines.

The SHM link from Chapter 12 is now explicit: each point in the medium executes local oscillation with the same frequency as the wave source, but phase differs between points separated in space. That phase pattern is what creates the moving shape.

A wave is longitudinal when particles oscillate parallel to the direction of energy transfer. Sound in air is the canonical case: air molecules move back and forth while regions of compression and rarefaction travel through the medium. Matter oscillates locally; the pressure pattern propagates.

Compression means molecules are temporarily closer than equilibrium, giving higher local pressure. Rarefaction means molecules are farther apart, giving lower local pressure. The alternation of these regions carries acoustic energy outward from the source.

Even in longitudinal waves, displacement graphs can be drawn with positive and negative values. Positive displacement means particle shift in the chosen positive direction. It does not itself mean compression or rarefaction unless phase relation to neighboring particles is considered.

Use displacement-distance graphs to read instantaneous spatial pattern and wavelength. Use displacement-time graphs to read period and frequency at one point. To infer propagation direction from two snapshots, check whether a fixed marker would need to move toward positive or negative displacement as time advances.

A strong exam habit is to mark one named particle and ask two questions separately: what is the wave doing globally, and what is this particle doing locally right now? Separating those answers prevents the classic confusion where students assign wave speed direction to particle velocity arrows.