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# Waves vs. particles

I mentioned above the word wave'' in several occasions. Since waves will appear repeatedly in the following I will take a short detour to explain what waves are and what are their properties. The American Heritage Dictionary defines wave as

A disturbance or oscillation propagated form point to point in a medium or in space

Thus when a stone is dropped on a calm pond we see a series of circular waves emanating form the spot where the stone hit the water, spreading out at a certain speed. If a bigger stone is used the water the waves become more pronounced, the distance form crest to trough becomes larger. If instead of dropping a stone we attach it to a rod and move it up and down we find that the faster we move it the closer together the crests and troughs of the waves; so that if we look at one point on the pond's surface we will see the water swelling and ebbing faster.

These characteristics of the waves have definite names; see Fig. 5.1,

• The frequency is the number of wave-crests that go through a point on the pond every second.
• The wavelength is the distance between two crests.
• The amplitude is the distance between crest and trough.

These properties, together with the speed at which the wave spreads characterize the waves.

Imagine a cork floating on the pond. As the wave goes by the place where the cork is floating it will boob up and down. Suppose that you measure the time it takes for it to go down from its highest point, down to its lowest and then back to its highest point again, then the frequency is the inverse of this time. So if the cork takes 0.5 seconds to go up and down and back up, the frequency would be 1/(0.5 sec) or 2 inverse-seconds. This is just a way of counting the number of oscillations per second: if each oscillation takes half a second, there will be two oscillations per second, and so the frequency is two inverse-seconds; a frequency of 7 inverse seconds indicates that there are seven oscillations each second, etc. There are many kinds of waves: water waves on a pond, sound waves in air (or water or any other medium), electromagnetic waves, etc.

Imagine now a calm pond with a few leaves floating on the surface. At one time a child drops a stone which makes a series of expanding circular waves. As they spread the waves eventually come to the floating leaves which bob up and down. The notable thing about this detail is that the leaves do not change position, even though the wave spreads, it does not carry the leaves with it. The same thing can be said of the water itself, the waves spread though it but do not carry the water along with them. In fact, if you look closely at the particles suspended in water (ponds usually have many of those) as the waves pass, they make circular motions about their initial positions but are not carried along. These waves use water as their propagation medium, in the same way as sound waves use air (or water or other materials) to propagate in. Without a medium these waves simply do not propagate: there is no sound in the vacuum. A reasonable question in connection with these observations is whether all waves need a medium to propagate in, the answer is (perhaps surprisingly) no!, and the way this was discovered is the subject of many of the following sections.

A particle is characterized by its mass and other measurable properties (for example, its charge). I will assume that this is intuitively clear. Ordinary everyday experience shows that waves behave very differently from particles . For example, if you are taking cover behind a wall form a person shooting peas at you, you will not be hit; yet when she screams that you are a chicken, you hear her perfectly well. Sound waves (and all waves in general) have the ability to go around obstacles (up to a certain extent: if the wall is very tall and wide the insults will not reach you); particles have no such ability.

The above properties of sound waves are well known. But, if light is a wave, should it not behave in the same way? And if it does, how come we do not see a person standing behind a wall (whom we can clearly hear)? I will now consider this (apparent) paradox.

Next: Light Up: The Clouds Gather Previous: Magnetism

Jose Wudka
9/24/1998