To describe with precision the parts of a wave, you have to consider its graphical representation. On the paper, a wave is drawn as a repetitive curved line with ups and downs, with a left-right direction. It’s usual to draw a straight line across the middle of the graphic, equidistant of the upper and lower peaks. The points that this line crosses, represent the instants when no movement is detected. The graphic illustrates the sequence of undulations that a wave produces throughout the air, a surface or the water. The undulant movement of a wave can be generated by the wind or by the displacement of an object attracted by the gravity or moved by other forces.

1. The Top and the Trough. The crest—or the top—of a wave is the upper point of each curve. Depending on variations of intensity, the representation of crest can vary its vertical position. The through—or the wave home—is the lower point of the curve. In other words, the crest is the farthest point from the middle line, in the upper position. And the through is the remotest point below the same middle line, called the medium. These complementary parts of a wave differ only in their up and down positions, also known as positive and negative displacements.
2. The Amplitude. The amplitude is strictly defined as the vertical line that connects a middle point, no-motion point, with the upper or lower point. However, as with the parts of the wave that were defined before, the amplitude can be positive or negative. It is positive when the amplitude represents the displacement from the medium to the upper point (the crest). And it is negative, when it describes the displacement toward the lowest point (the through). Nevertheless, you are able to determine the amplitude in every point, not only the crest or the through, but when the wave is increasing or decreasing its intensity.
3. The Length. One of the parts of the wave that measure the extension of the cycles is the wave length. The length of a wave is more frequently calculated from a crest to the following or from the through to the next one. However, in some cases, it can be measured from any point within the wave displacement to the next point, from left to right. Of course, as the length is represented by a horizontal segment, the second point will be in a corresponding position with relation to the first one.
4. The Frequency. A wave cannot be totally represented by a still graphic. This is because any vibratory movement has an associated speed. Because of that, we have to consider the frequency as one of the parts of a wave. You can define as a “cycle”, the complete trajectory from one upper point to the following. Then, the frequency is the number of cycles by the unit of time. This is similar to tell the speed of the wave. For Physics, one cycle by second is equivalent to one Hertz.
5. The Energy. Although the energy that a wave transports is not a line on a graphic, you should consider this element as one of the parts of a wave. The motion of a wave transports energy without any object, though that motion could have some effects on matter. The energy of a wave has direct relation with the amplitude. For a long amplitude wave, you will have a higher energy. A short amplitude wave is associated to lower energy.