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# 1. What is a Wave?

• Contributed by Wendell Potter and David Webb et al.
• Physics at UC Davis

# Primitive Wave Concepts

There are two important goals associated with the first part of this unit. Firstly, to become familiar with wave phenomena and how we analyze them, and secondly, to sufficiently understand the mathematical representation of one-dimensional harmonic waves. We want to use this mathematical representation as a tool throughout the rest of the course to help us understand the physics of sound and light waves.

A material wave is a very common type of internal motion of a material substance, called the medium of the wave. In order for material waves to exist there must be forces between neighboring particles in the medium. We will examine how a disturbance travels and gives rise to wave-like behavior by coloring a medium three different pieces and labeling them as sections 1, 2 and 3.

The “displacement” of the medium in section 2 is pulled down by sections 1 and 3. Thus section 2 will accelerate downward, back toward equilibrium. By Newton’s third law section 2 must exert an equal and opposite force $$\textbf{F}_{\text{2 on 3}}$$ on section 3. This will cause section section 3 to accelerate upward, so a little time later section 3 is displaced like section 2 was. In this way, the disturbance has traveled from section 2 to section 3 without the individual pieces of medium traveling along with it!

You may wonder why the sections exert a force on one another at all – the origin of this force can be traced back to the fact that the individual atoms have a preferred separation distance, and resist being pushed or pulled to maintain that preferred distance. Stretching or compressing the medium causes the atoms to exert forces on their neighbors, and to resist forces exerting on them. We have simply clumped atoms together into three sections for convenience – this same discussion applies to individual atoms! The restoring forces responsible for wave behavior are typically strongest in solid materials and weaker in gaseous materials.

There is one small detail that you may be wondering about – by Newton’s third law there must be a upward force $$\textbf{F}_{\text{2 on 1}}$$. Why does the pulse not travel in both directions? Consider that the displacement was previously in section 1; to return to the level in the picture, section 1 must have traveled down. From Newton’s first law we know that if there was no net force acting on section 1 it would keep travelling downward. It comes to rest precisely because there is an upward force $$\textbf{F}_{\text{2 on 1}}$$!

This explanation for a wave shows that the concepts we introduce when discussing material waves are no different from the concepts that we have already introduced when discussing forces, motion and atoms. We place such an emphasis on waves because dealing with the form of a wave is often easier than trying to visualize force diagrams for many different sections of a medium. Eventually we will encounter non-material waves, and this previous exposure to disturbances in material waves will be an invaluable guide.

The disturbance (or, more technically, an oscillation) may be spread throughout the medium and recur continuously at each point (called a "repetitive" wave) or the oscillations may exist for only a limited time at each point (a "pulse-type" wave). The material wave that we have divided into sections above is an example of a pulse-type wave.

Waves in a medium are started by outside forces that act on some of the particles in the medium to start them oscillating. External forces are not required to keep a wave going once it has been started. Consider a water wave on the surface of a pond; a rock dropped into the pond is the outside disturbance that starts wave motion. Once started, the ripples expand outward on their own. We don’t have to continue dropping rocks into the pond to keep the ripples moving.

# A Refined Definition of Waves

It is difficult to come up with a general definition for a "wave." For the moment we will content ourselves by looking at the definition of a material wave:

A material wave is the large movement of a disturbance in a medium from its equilibrium position, whereas the particles that make up the medium move very little.

Let’s consider this definition more closely. A wave is the movement of something. What is it that moves? Consider ripples expanding in a pond. While there is some movement of the individual water molecules, they merely bob up and down and they do not travel. It is the ripples that move significantly. The movement of the ripples across the surface of the water is what we mean by a "wave". It is not the movement of the individual water molecules, or the disturbance of the surface of water from equilibrium, but rather the movement of the disturbance to different locations in the medium that we call the wave. Example #1 should help clarify this point.

Example #1

Here is an example that will demonstrate the difference between particles of the medium moving versus a disturbance in a medium moving. Take a bowl of water, and tip a small amount of olive oil on the surface, so that you have a set-up like picture below (If you don't have a bowl of water or oil, you can make this a thought experiment).

If you oscillate your hand gently at the location $$x$$, do you get waves at the location $$y$$? Do you end up with oil moving to the location $$y$$?