WavesTransverse and Longitudinal Waves
At Eden Gardens the crowd starts a Mexican wave. Each fan only stands up and sits down again, yet the wave races right round the stadium. After the match the crowd queues at the exit gate, and when someone at the back gives a shove, the push travels forward from person to person along the queue. Both are waves, but the people move differently in each.
The particles of the medium oscillate as a wave passes. If they oscillate perpendicular to the direction in which the wave travels, the wave is transverse. If they oscillate along the direction of travel, the wave is longitudinal. Below is one medium, a block of particles. Shake its left end each way and follow the amber particle.
In the transverse wave the amber particle moves straight up and down, at right angles to the green arrow, and the wave has crests and troughs. In the longitudinal wave the same particle moves back and forth along the arrow, and the particles bunch up into compressions (C) and spread out into rarefactions (R). In both, every particle stays near its own place; only the pattern travels.
A wave on a string (Figs. 14.2 and 14.3 of your book) is transverse: one flick of the end sends a single pulse, and a steady up-and-down shake sends a sinusoidal wave. Sound in a pipe pushed by a piston (Fig. 14.4) is longitudinal: one push and pull sends a pulse of compression and rarefaction, and a steady push–pull sends a sinusoidal train. All of these are travelling or progressive waves, because the disturbance travels from one part of the medium to another while the medium as a whole stays put. A stream is water moving as a whole and a wind is air moving as a whole; a water wave and a sound wave are disturbances moving through water and air that stay where they are.
There are two ways to look at any wave, and you will use both. Freeze the time, and you see the shape of the whole wave at that instant. Watch one spot, and you see how a single element of the medium moves in time.
What Earthquakes Reveal
In a transverse wave each layer of the medium slides sideways past the next one: the medium is sheared. Only a medium that resists shearing can pass a transverse wave on, and that means a solid. Liquids and gases simply flow when sheared, but they do resist being squeezed, as every elastic medium does. So:
- longitudinal waves travel through solids, liquids and gases;
- transverse waves travel only through solids (plus along stretched strings, and on the surface of water, as you will see next).
Steel carries both kinds; air carries only longitudinal waves. An earthquake sends both kinds into the Earth: P waves, which are longitudinal and fast, and S waves, which are transverse and slower. Seismograph stations all round the globe record them. Send each kind from the earthquake and see which stations it reaches (the rays are drawn straight; in the real Earth they bend).
The S waves stop dead at the edge of the outer core, while the P waves cross it. What does that tell geologists about the outer core?
Only a liquid would let P waves through and stop every S wave, so the outer core must be liquid. That is how we know what lies thousands of kilometres under our feet without ever going there. The two seismic waves also show a general rule: transverse and longitudinal waves usually travel at different speeds in the same medium. In rock, P waves are about 1.7 times as fast as S waves, so a seismograph always records the P waves first.
A Leaf on a Wave
The surface of water carries two kinds of waves. Capillary waves are ripples a few centimetres long at most; the force that flattens them again is the surface tension of the water. Gravity waves are several metres to several hundred metres long; here gravity pulls the raised water back to its lowest level. The water in a gravity wave does not move only at the surface: the motion reaches all the way to the bottom, getting weaker with depth. Watch the particles of water as a gravity wave passes.
How does the amber leaf floating on the surface move?
Each particle of water goes round in a circle, forward under a crest and backward under a trough, and the circles shrink with depth. Up and down is a transverse motion and back and forth a longitudinal one, so waves on the sea are a combination of transverse and longitudinal waves.
Example 14.1
Example 14.1 For each wave below, decide whether the motion is transverse, longitudinal or a combination of both. Drag each one into its bucket.
Answer A rope or a string carries transverse waves. Oil pushed by a piston and air set vibrating by a crystal can carry only longitudinal waves. The wake of a boat is a surface wave on water, a combination of both. The sideways kink in a loose spring is the subtle one: the coils move sideways, but they also bunch up and spread out along the spring as the kink passes, so it too combines transverse and longitudinal motion.
Speed Round: Transverse or Longitudinal?
Transverse: the medium moves across the direction of travel; it needs a solid, a stretched string or a liquid surface. Longitudinal: the medium moves along the direction of travel, in compressions and rarefactions, through any elastic medium.
Get five right to move on.