It is good practice to check an equation's units for consistency.


frequency = cycles/sec =


Figure 2.7 shows another way of looking at the time behavior of a rotating vector. It can be thought of as an auger boring its way through phase space. If we look at the auger from the side, we see the sinusoidal trace of the passage of its real amplitude. If we look at it end on, we see the rotation of its radius vector and the circular progression of its phase angle.

Changes in Phase

If a second waveform is drawn on our graph in Fig. 2.8 immediately below the first, we can compare the two by examining their values at any particular time. If they have the same frequency, their peaks and valleys will occur at the same intervals. If, in addition, their peaks occur at the same time, they are said to be in phase, and if not, they are out of phase. A difference in phase is illustrated by a movement of one waveform relative to the other in space or time. For example, a n/2 radian (90°) phase shift slides the second wave to the right in time, so that its zero crossing is aligned with the peak of the first wave. The second wave is then a sine function, as we found in Eq. 2.6.

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