WavesIntroduction

Drop a pebble and keep your eye on the diyas. One unit of the picture is one centimetre of pond.

The ripples crossed the whole pond, but the diyas did not go with them. Each one only rode up and down on the spot: its amber trail is a short vertical line. What travelled across the pond was a pattern of disturbance, not the water. A pattern that moves through a medium without carrying the medium along with it is called a wave.

The same thing happens when you speak. Your voice reaches a friend across the room, but no air flows from your mouth to their ear: the air next to you is squeezed and stretched, it squeezes and stretches the air beyond it, and the disturbance is handed on. Waves carry energy and information from place to place without carrying matter. Every conversation and every phone call depends on this. A phone call even swaps one kind of wave for another: sound becomes an electric signal, the signal becomes a radio wave, and the steps run in reverse at the other end.

Three Families of Waves

Not every wave needs a medium. Starlight that left its star hundreds of years ago crosses almost empty space to reach us. Waves come in three families:

• Mechanical waves: waves on a string, water waves, sound, seismic waves. They need a material medium and cannot cross a vacuum, because they travel by the particles of the medium pushing and pulling on each other.
• Electromagnetic waves: light, radio waves, X-rays. They need no medium. In a vacuum all of them travel at the same speed, c = 299 792 458 m s⁻¹ (Eq. 14.1). You will study them in Class 12.
• Matter waves: waves that belong to electrons, protons, neutrons, atoms and molecules, which come from quantum mechanics. Electron microscopes already put the waves of electrons to work.

Sort these waves into their families.

This chapter is about mechanical waves. Waves have inspired poets and painters for thousands of years, but their scientific study began only in the seventeenth century, with Christiaan Huygens, Robert Hooke and Isaac Newton. It grew out of the study of oscillations, of masses on springs and simple pendulums, because a wave in an elastic medium is really a chain of oscillations handed on from one particle to the next. Stretched strings, coiled springs and air are all elastic media.

Springs All the Way Down

Fig. 14.1 of your book shows a row of springs joined end to end. Pull the first one suddenly and let go: the disturbance runs to the far end, though each spring only stretches and squeezes a little about its own length. A train standing at a platform is the same system. Its coaches are joined by spring couplings, so when the engine gives a sudden push, the push is handed from coupling to coupling down the train. Give the engine a quick push and pull, and watch the bars under the train.

The last coach moved well after the engine did, and no coach moved more than a few centimetres. The bump in the bars is the disturbance on its way: each coupling squeezes the next coach, which squeezes the coupling after it, and so on down the train.

Air passes sound along in the same way. A sound wave squeezes a small region of air, raising its density by a little, δρ, and with it the pressure, by δp. Pressure is force per unit area, so the squeezed region pushes back like a compressed spring. Its molecules crowd into the next region and compress that, while the first region thins out into a rarefaction; a thinned-out region, in turn, draws in air from its neighbours. Compressions and rarefactions are handed on, and the disturbance travels. A crystalline solid works the same way: every atom sits in equilibrium among its neighbours, and if one is pushed, the others push back like springs. So we can picture any elastic medium as particles joined by springs.