## Introducing Waves

What is a wave? Waves are so diverse that we might tend to regard different types of waves as separate entities, unrelated to one another. Do events such as the devastation of a region by an earthquake and the melodic tones of a musical instrument have anything in common? In this chapter we explore the common ground between these and many other phenomena.

Waves carry energy from one place to another. They also act as messengers, transmitting information. We look at different types of waves, how they are created, what they are 'made of' and how they carry out their functions of carrier and messenger.

To deal with some aspects of wave behaviour, we need to express the properties of the waves mathematically. We can then make quantitative predictions regarding many wave-related phenomena seen in nature. In a mathematical analysis of waves, it is most convenient to use the simplest type of wave form — a continuous sine wave. It is gratifying, if rather startling, to find that even the most complicated periodic waves can be constructed simply by adding a number of these sine waves.

6.1 Waves — the basic means of communication

When talking about waves, we most likely picture a seaside scene with ocean waves approaching the shore or perhaps a ship at sea tossed in a storm. A survey asking the question 'What serves as the most common means of communication?' would be unlikely to favour the answer 'Waves'. Yet, heat and light from

Waves coming in on a beach. Courtesy of Johntex.

the sun are carried by waves. We could neither see nor speak to one another were it not for light waves and sound waves. Even the sensation of touch relies on the transmission of nerve impulses, which are composed of wave packets.

Electromagnetic waves, which pervade all space, and without which the universe could not exist, are the basic theme of this book. Light is just one member of that family. These waves propagate in a mysterious way, as we shall see in later chapters.

We have learned to produce electromagnetic waves and to put them to a variety of uses, many of which are now taken almost for granted. Radio waves facilitate the remote communication that enables us to hear and to see the latest news and to watch our favourite television programmes. We can receive information about the lunar surface from space probes. In medicine, lasers produce waves for keyhole surgery, X-rays are used in diagnostic imaging and radiation therapy; infrared waves heat muscles and relieve pain. Microwaves cook food; radar waves guide planes and ships. Last but not least, a tiny infrared beam from our remote control allows us to change channels without leaving our armchair in front of the TV set!

Once we become aware of the seemingly endless variety of waves, it begs questions such as: Do all waves have something in common? How can we deal with waves mathematically? What is the justification to say that light behaves as a wave?

### 6.1.1 Mechanical waves in a medium

When a medium is disturbed by a wave, individual particles oscillate about their equilibrium positions and transmit energy by their mutual interactions.

A stone dropped into the middle of a pond gives rise to waves spreading out on the surface of the water in ever-increasing circles. The expanding waves show that something definitely propagates, but it is not the water itself; ducks sitting in the path of the wave bob up and down but do not necessarily move in the apparent direction of propagation. Energy contained in the local oscillations of individual water particles is transmitted with no net motion of these particles from the middle of the pond to its edge.

Waves transmit energy, momentum and information from one place to another by means of coordinated local oscillations about an equilibrium position.

Waves, whether naturally occurring or artificially produced, can be classified according to the type of disturbance which is transmitted and also by the relationship between the direction in which things change locally and the direction of energy transfer.

When molecules are stimulated by an external force which varies periodically (repeats itself at regular intervals), they vibrate and a mechanical wave is set in motion. Individual molecules remain localised, but energy is transferred from molecule to molecule and hence from one place to another. The energy is

Surface waves created by dipping a stick into water. Courtesy of Roger McLassus.

transmitted through the material by molecular interactions but the precise nature of the interaction depends on the material. On the macroscopic scale, we refer to the level of the molecular response as the elasticity of the material.

Mechanical waves are propagated by the interaction of molecules with their neighbours and do not exist in a vacuum.

### 6.1.2 Transverse waves

Energy may be transmitted by particles oscillating in a direction either perpendicular or parallel to the direction of energy transfer. In the disturbance caused by the stone, the water surface moved up and down, but the wave moved horizontally. This sort of wave is called a transverse wave.

A transverse wave is a wave for which the local disturbance is perpendicular to the direction of propagation of energy.

We need some form of bonding to support a transverse wave. When molecules are bonded together, transverse waves can propagate. The bonding must be such that, when a molecule moves up and down, it tends to drag neighbouring molecules with it. Force is required to disturb the molecule and the phenomenon is technically known as resistance to shearing stress. Such bonding exists in solids and liquids.

In a row of children holding hands, if one child jumps up, the children on each side will be pulled up. The bonding is in the holding of hands.

There is no bonding if the children do not hold hands and the jumping motion of one child does not affect the others.

The 'Mexican wave', often seen at sporting events, is another example of a transverse wave.

### 6.1.3 Longitudinal waves

Transverse waves cannot propagate in gases, because gases have practically no resistance to shearing stress. Air molecules are much further apart than the molecules of a solid or liquid, and as a result the viscous forces tending to drag adjacent layers of air are too small to propagate a transverse disturbance. There are, however, forces between the molecules which resist compression. A fully laden bus is supported by the compressed air in its tyres; a hovercraft rides on a cushion of compressed air.

In 1887, John Dunlop developed the pneumatic tyre for his son's tricycle, and patented it in 1889. The patent description

Courtesy of The Hovercraft Museum Trust.

read: 'A device covering the circumference of a wheel. It cushions the rider from a bumpy road, reduces wear and tear on the wheels and provides a friction bond between the vehicle and the ground.'

A pulse of compressed gas or a series of such pulses is transmitted through a gas at a speed which depends on the elastic properties of the gas and on its temperature. The human ear is a delicate instrument which can detect such compressions. We call this sensation sound.

The mechanism of transmission of a longitudinal pulse can be shown by the example of an orderly queue of people waiting for a bus.

As the bus approaches, the people at the back of the queue begin to push the people in front of them. By the time the bus stops, the compression has been transmitted to the front of the queue. Individual people move in the same direction as the compression.

Sound waves propagate as a series of compressions. A vibrating membrane such as a guitar string exerts a varying pressure on the adjacent air and the pressure variations are transmitted as a longitudinal wave.

A longitudinal wave is a wave where the local disturbance is parallel to the direction of propagation of energy.

In a solid each molecule is bonded to all of its neighbours, so the application of a force in any direction will distort the equilibrium arrangement. This means that solids can transmit both transverse and longitudinal waves. An underground explosion, for example, generates both transverse and longitudinal seismic waves which are transmitted through the earth. The production of simultaneous longitudinal and transverse waves can be demonstrated using a slinky, as illustrated in Figure 6.1.

transverse wave

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