Transverse and Longitudinal Waves

Mechanical waves are classified into two kinds according to the relation between the direction in which the medium's particles vibrate and the direction in which the wave itself propagates. In a transverse wave, each particle of the medium vibrates perpendicular to the direction of wave propagation -- as the wave moves along the x-axis, say, each particle moves up and down (or side to side) about its mean position. The waveform, at any instant, shows a series of crests (points of maximum positive displacement) and troughs (points of maximum negative displacement). A transverse wave can be set up and sustained only in a medium that can support shear stress -- that is, a medium whose layers resist being slid sideways past one another -- which is why transverse mechanical waves travel readily along a stretched string or across the solid body of a rod, but (aside from surface effects) cannot propagate through the bulk of a fluid such as air or water, since a fluid offers essentially no resistance to shear. In a longitudinal wave, by contrast, each particle of the medium vibrates back and forth along the very same direction in which the wave propagates. Rather than crests and troughs, the waveform at any instant shows alternating regions of compression (where particles are momentarily crowded closer together than normal, and pressure/density is locally higher) and rarefaction (where particles are momentarily spread farther apart, and pressure/density is locally lower). A longitudinal wave needs only volume (bulk) elasticity to propagate, not shear elasticity, …