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I stood firmly on the sandy beach, facing the vast blue ocean, from where majestic waves surged incessantly and in complete indifference to my presence. They beat powerfully on the long shoreline, like a furious army charging at a defiant enemy, but only to die away into foamy puddles that meekly receded back. My legs became wet when the cool waters climbed over my frame, as they tried to uproot me from my vertical posture.

They were noisy, those waves, splashing on and on with never-ending persistence. They have been doing this day and night, summer and winter, since time immemorial: long before humanity emerged on earth! They care not if people are swimming near where they lash on the land, they care not if petty creatures make a living here and there.

Periodicity is what strikes one most about waves, their routine repetition to and fro. Starting somewhere, those waves moved across to reach somewhere. This was motion in the ocean, not of the ocean. In essence, a wave is the propagation of a periodic disturbance from one region of space to another. Disturbance is motion, and motion is energy. So waves are a means for transporting energy. This is often their function: to transport energy from place to place, faster and more efficiently than other modes.

Take a long slinky and place it on a smooth floor. Press it gently at one end and the compression will slowly travel to the other. A disturbance has been propagated from one region of space to another: We have a wave. Here, the oscillations are along the axis of the spring, and so is the direction of propagation of the wave. Such a wave we call “longitudinal” because its expression is entirely along a length. Longitudinal waves tend to arise in media where the elements are not in direct contact with one another—as in air, for example. Sound is a longitudinal wave. An earthquake disturbance has longitudinal waves: The rocks are forced to vibrate in the direction of propagation of the wave.

In waves on water, the motions of the medium are up and down while the wave itself is propagating horizontally. The line of oscillation is perpendicular to that of propagation. This is an example of a transverse wave. We may make the rope oscillate up and down at one end, and the wave propagates along the rope. A transverse wave again. But we could also make it oscillate right and left. Indeed, the oscillation may be along any line perpendicular to the rope. If, however, the rope were to pass through a narrow slit, then the line of oscillation is restricted. Then the transverse wave is said to be “polarized.”

Stand in an open field and clap your hands. There is no one to hear, none to respond. Let it be a region where a high hill stands, and you will hear the clapping again. The sound that bounces back is an echo we say, a prompt reflection of the sound wave. All waves reflect back when they encounter an obstacle. A simple property, but causing such richness in our experience! It is the reflection of light from a polished mirror that enables us to see ourselves. If there were no reflections, we could never know how we looked unless we relied on paintings or photographs.

When waves reflect, they follow laws, precise and mathematical. Sometimes reflection causes peculiar effects: like the mirage on a hot sandy desert that makes us see images of palm trees below them at a distance, creating the illusion of a calm pool. The laws of reflection also trap light inside some crystals, which then release it with such a sparkle it becomes a symbol for love and engagement, for that is what a diamond does. It is thanks to the reflection of radio waves from the upper sheets of the atmosphere that our tuners pick up broadcasts from distant lands. Also, our satellites reflect microwaves and make intercontinental TV and communication all so easy. Yes, there are myriad situations, emerging in nature or human devised, where the reflections of waves create scenes and spectacles that otherwise would never be there in the world.

If we wish to play the game of fruitful physics seriously, we need to measure, we need quantitative descriptions. This means we should attach numbers to waves. We call a full movement of up and down a complete cycle. Now we can talk of how long it takes for a wave to make one full cycle. This is the period of the wave. A wave that takes two seconds for a rise and fall has a period of two seconds. We may count the number of cycles in a second. We call this the frequency of the wave, and measure it in units called hertz (Hz). We measure how high the wave rises and call this its amplitude. If the wave rises to a maximum height of 2 meters, this is its amplitude. We may reckon how far the disturbance travels in a second. This is the velocity of propagation of the wave. If the wave travels 3 meters in a second, its velocity of propagation is 3 meters per second or 10.8 kilometers per hour.

This is physicists’ jargon on waves. They speak of its period, frequency, amplitude, and velocity. Numbers are not just for the tagging: They often mean a good deal more.

A wave with a single frequency and period is a pure wave, such a one we can only picture—a Platonic ideal, as it were. In the crass world of physical reality, things are seldom so simple: Here we only observe overall effects, the jumbling up of myriad factors to make interesting blobs. That is what makes complexity the central theme when it comes to studying matters of immediate importance to us.

Most waves in the world are in fact complex—mixtures of a great many waves of different frequencies. They add up as per an innate law of wave-addition and become one total effect. In the observed experience, it may in no way be clear that what appears is a combination. It is somewhat analogous to a fruit punch: sweet and flavorful, a single homogeneous satisfying beverage, but constituted of a variety of juices of different tastes. So we see white light, which in truth is a combination of light of all the rainbow hues. We hear a sound, a call or a sustained tune, and we perceive it as one complete sound, but in fact, it is made up of a great many sound waves of a great many frequencies.

Yes, the world of waves is always that way: never pure and simple, always complex and combined. This in itself is a significant recognition. But what is equally remarkable is that we have means and methods for analyzing a complex wave into its component parts. We do this at the physical level through all sorts of instruments—spectral analyzers, they are sometimes called. They are like machines into which you shove a heap of coins and out come pennies and nickels, dimes and quarters, all neatly sorted. Complex waves can also be analyzed through mathematical techniques known as Fourier analysis. Such analysis is essential in a great many contexts, as in the construction of filters for our sound systems.

This is the sort of reductionism that the new philosophies are up against. Oh, it is all so misdirected, so narrow, so distorted, the holists cry out: those narrow classical physicists, those unweavers of the rainbow, misguided in their enthusiasm for the analytical mode, to the vivisection of nature, which is to be grasped in its totality. The point is, both are important modes. You need the holistic approach for uncovering certain aspects of perceived reality. You absolutely need the analytical, reductionist approach to know white light is made up of primary colors or that gross matter is made up of quarks. Reductionism gives us profound insights into the roots of perceived reality, as does holism; food gives us great satisfaction, as does knowledge of vitamins and proteins.

I stand in the field and call my friend whom I spot walking away at a distance. She does not turn her head. What happened to all my sound? It got dissipated as it traveled the distance. The energy of the wave diminishes little by little as it passes through a medium. The wave attenuates: Its amplitude gets less and less along its course.

Attenuation causes water ripples to die off when we fling a stone in a pond. Attenuation is like the gradual slowing down of an oscillating pendulum, which ultimately ceases oscillating when all its energy is lost to the medium.

There is no material medium between us and the stars, so their lights travel light-years of distance, unattenuated. If there was matter in the interstellar separations to absorb a little of the light energy passing through them, as some glasses do, then very quickly stellar emanations would die away, and there would be but pitch darkness in the night sky. Then all astronomy would be impossible, we would never have known of the splendor and extent of the universe. Perhaps we would have formulated a very different physics and cosmology.

There are many more properties of waves, like interference, diffraction, and polarization, each causing the world to strike us the way it does. Bereft of even one of these properties, we would be experiencing a very different world. We are immersed in seas of waves—not just of the light and sound that please our perceptions, but many more to which our senses don’t respond. There are a great many waves aside from waves on water, brain waves, gravitational waves, and matter waves. They all play a role in the phenomenal world, some overt and obvious, some subtle and not apparent at all. But the untiring ingenuity of science has put them all into evidence, and has enabled us to utilize them for human ends.