A particularly simple kind of wave, the sine wave, is illustrated in figure 1.2 . The oscillatory behavior of the wave is assumed to carry on to infinity in both positive and negative directions. Notice that the wavelength is the distance through which the sine function completes one full cycle. The crest and the trough of a wave are the locations of the maximum and minimum displacements, as seen in figure 1.2 . So far we have only considered a sine wave as it appears at a particular time.
All interesting waves move with time.
The movement of a sine wave to the right a distance may be accounted for by replacing in the above formula by . If this movement occurs in time , then the wave moves at velocity . We normally think of the frequency of oscillatory motion as the number of cycles completed per second. This is called the rotational frequency , and is given by . It is related to the angular frequency by .