How Waves Carry Energy Without Carrying Matter Away

Drop a pebble into still water and ripples spread outward. A floating leaf may bob up and down, but it does not race to the edge of the pond with the ripple. The water moves mainly around its local position while the pattern of disturbance travels across the surface.

Many waves behave this way. In a rope, each section moves as a pulse passes. In sound, air particles vibrate back and forth while pressure changes move through the air. The wave transfers energy through interactions between neighbouring parts of the medium.

A medium is the material through which a mechanical wave travels. Water waves use water, sound can use gases, liquids or solids, and a stretched rope carries a pulse through its fibres. Mechanical waves cannot travel through a perfect vacuum because there are no particles there to pass the disturbance along.

In a transverse wave, the movement of the medium is at right angles to the direction the wave travels. A wave on a rope is a common example. The pulse travels horizontally while pieces of rope move up and down.

In a longitudinal wave, the movement is parallel to the direction of travel. Sound in air creates alternating regions where particles are crowded together and spread farther apart. The particles vibrate back and forth, while the pressure pattern moves onward.

Real water waves near the surface involve more complicated circular or oval motions, so they are not perfect versions of either simple type. Models still help because they let you focus on one feature at a time without pretending nature signed a contract to remain tidy.

Amplitude measures the size of the disturbance. A larger amplitude usually means the wave carries more energy. Frequency tells you how many complete cycles pass a point each second. Wavelength is the distance between matching points, such as crest to crest. Wave speed depends on the medium. Tightening a rope, changing water depth or warming air can change how quickly a disturbance travels, even when the source keeps vibrating at the same frequency.

Try reading any wave diagram in this order:

• •Find the resting or middle position.
• •Measure how far the wave moves from that position.
• •Locate one complete repeating cycle.
• •Check the direction of travel.
• •Ask what is moving locally and what energy is moving onward.

A crowd wave at a stadium is a neat model of a travelling disturbance. Each spectator stands up and sits down in place, yet the pattern races around the ground. Nobody moves from one seat to the next, but something clearly travels. If people react more quickly, the wave moves faster. If a section stays seated, the wave can fade or stop. The crowd is acting as the medium, and each person passes the disturbance to their neighbour.

A tsunami shows how the medium changes a wave. In the deep open ocean, a tsunami can have a height of well under a metre but a wavelength of many kilometres, and it travels as fast as a jet aircraft. A ship may barely notice it passing. As the wave reaches shallower water near a coast, it slows down. The energy that was spread through a deep column of water becomes concentrated, the wavelength shortens and the wave height grows dramatically.

Speed, frequency and wavelength are tied together by one relationship: wave speed equals frequency multiplied by wavelength. If a wave source vibrates more often while the speed stays fixed, each wave must be shorter. Sound in air at room temperature travels at roughly 340 metres per second. The note A used to tune many orchestras has a frequency of 440 hertz, so its wavelength is about 340 divided by 440, or just under 0.8 metres. A deep bass note at 40 hertz has a wavelength of more than eight metres.

You can use the speed of sound during a thunderstorm. Lightning and thunder are produced at the same moment, but light reaches you almost instantly while sound takes about three seconds to cover each kilometre. Count the seconds between the flash and the rumble, then divide by three to estimate the distance in kilometres. A gap of nine seconds puts the strike about three kilometres away. Ships use the same idea with echo sounding, timing how long a sound pulse takes to bounce off the seabed and return.

Unlike two balls, two waves can pass straight through each other. Where they overlap, the disturbances simply add together, a rule called superposition. If two crests meet, the medium briefly rises higher than either would alone, which is constructive interference. If a crest meets a trough of the same size, they cancel and the water or rope sits flat for an instant, which is destructive interference. Once they have passed, each wave continues on its way with its original shape, as if the meeting never happened. You can see this by sending pulses from both ends of a long slinky or rope.

Noise-cancelling headphones put destructive interference to work. A tiny microphone picks up steady background sound, such as the drone of an aircraft engine, and electronics produce a matching wave with its compressions and rarefactions swapped. Played through the speaker, it largely cancels the noise at your ear. This raises a fair question: if waves cancel, where does the energy go? It is not destroyed. When two rope pulses cancel, the rope is flat but still moving, so the energy is briefly all kinetic. In wider patterns, quiet zones are always balanced by louder zones elsewhere, so energy is redistributed rather than lost.

The energy a wave carries grows much faster than its height. For many kinds of wave, energy is proportional to the square of the amplitude, so doubling the amplitude carries four times as much energy, and tripling it carries nine times as much. Ocean waves show this clearly. A swell 2 metres high carries about four times the energy along each metre of its crest as a swell 1 metre high with the same period. This is why a storm sea with waves only a little taller than usual can do so much more damage to sea walls, ships and beaches.

Energy also thins out as a wave spreads. Sound from a small source travels outwards in every direction, sharing its energy over the surface of a growing sphere. That surface area increases with the square of the distance, so at twice the distance the intensity falls to a quarter, and at ten times the distance to a hundredth. This is called the inverse square law. A ripple on a pond spreads only across a flat surface, around a circle whose length grows in simple proportion to distance, so it fades more gently. A laser keeps its beam narrow, which is why its brightness hardly drops across a room.

Waves transfer energy through repeating disturbances. Matter usually vibrates or moves locally while the wave pattern travels farther. Separate those two motions, and water ripples, sound and many other wave behaviours become much easier to picture.