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# 10.5 Properties of Waves

Sinusoidal wavesÂ of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time. Click here for original source URL

Plot of a sine wave, showing three pairs of corresponding points between which wavelength (lambda) can be measured. Click here for original source URL.

For convenience, we can think of light and other forms of electromagnetic radiation as waves that carry energy from one place to another. Electromagnetic radiation is a repeating or periodic phenomenon with wave properties. Let's look at it in more detail. We can describe any wave motion by four numbers, two of which are related to each other. The distance between two successive crests (or troughs) is the wavelength. The number of crests (or troughs) that pass a fixed point every second is the frequency. The wavelength and frequency of any wave are two measures of the same thing; multiplying them gives the velocity of the wave.

1 = Amplitude (peak), 2 = Peak-to-peak, 3 = RMS, 4 = Wave period. Click here for original source URL.

Another important number is the amplitude of the wave, usually shown as half the height of a wave from peak to trough. A wave is a disturbance and the amplitude quantifies the amount of the disturbance. For example, the amplitude of a water wave is the amount by which the wave deviates above or below a smooth undisturbed surface. For a sound wave, the amplitude is the amount by which the air density goes above or below the average density. In the case of light or other electromagnetic waves, the amplitude is given by the positive or negative amounts of electric or magnetic force. A more useful quantity is intensity, or the strength of the wave that we actually measure. The intensity of the radiation is proportional to the square of the amplitude of the wave.

Here is a useful analogy for remembering an important point about wavelength and frequency: the two have an inverse relationship. Imagine trains traveling at the same speed but with different length cars. The shorter the cars (smaller wavelength), the more cars that pass per second (higher frequency). Conversely, a smaller number of long cars (longer wavelength) pass each second (lower frequency).

All electromagnetic radiation travels at the same velocity in a vacuum, 300,000 kilometers per second (186,000 miles per second). This universal physical constant is the speed of light and it is given the symbol, c. Remember that the speed of light is also the speed of all other types of electromagnetic wave in a vacuum. (We should note, however, that light traveling through air or glass or any other transparent medium travels at different, slightly slower speeds.) It is a striking fact that all electromagnetic waves travel at the same speed in a vacuum. To use the analogy just given, imagine that we have trains with cars of an enormous variety of size traveling at the same speed. The number of cars passing per second (frequency) goes up at the same rate that the size of the cars (wavelength) goes down.

How can we ever measure such an amazingly large number as the speed of light? Galileo was a masterful experimenter and he tried to measure the speed of light nearly 400 years ago. One night, he stationed a friend on a hilltop several miles away. Both Galileo and his colleague had lanterns with a shutter that could be lowered over the light. They planned that when Galileo sent a flash of light between the hilltops, his friend would immediately respond with a flash from his lantern. Galileo tried to measure the time for a light signal to make the round-trip between hilltops, but he soon realized that it was too short to measure. Light apparently traveled many miles in a second. Beyond that, Galileo could say no more.

Portrait of the Danish astonomer Ole RÃ¸mer. Click here for original source URL.

The first real measurement of the speed of light used an ingenious observation by the Danish astronomer Ole Roemer in 1675. Roemer began with Galileo's careful observations of the moons of Jupiter. As the moons move in their obits of Jupiter, it is possible to carefully time the moment when they pass behind Jupiter and are eclipsed. Roemer discovered that the eclipses occur slightly earlier when distance between the Earth and Jupiter is shorter. The reason is that the light takes a shorter time to travel the shorter distance to our eyes. Roemer deduced that it takes 11 minutes for light to cross the distance between the Earth and the Sun; the actual number is 8 minutes but his logic was correct. You can see here an echo of the ancient Greeks who use logic and geometry to learn about the nature of the universe. Roemer's observations provided additional evidence that the Earth was in motion around the Sun. Modern laboratory measurements give a very accurate value for the speed of light. With a prodigious speed of 299,792 kilometers per second, it is no wonder that light seems to travel instantaneously in the everyday world.

Waves carry energy from one place to another. The everyday world contains some remarkable examples of the ways that wave energy can be transformed from one kind to another. It is an important principle of physics that energy is conserved — it can change forms but never just appear or disappear.