Vector Addition

Since one vector represents one sinusoid, to add two sinusoids of the same frequency, we need only perform vector addition.

Figure 11: Adding sinusoids using vector addition.

$\scalebox{1}{\includegraphics{eps/vect_add.eps}}$
Since the vectors have the same frequency, they will rotate as a unit and their sum will have the same frequency.
The sum vector U + V in Figure 11 also has its own x and y component (from projecting onto the x- and y-axes) and therefore may have a different amplitude and phase.

**Figure 11:** Adding sinusoids using vector addition.
$\scalebox{1}{\includegraphics{eps/vect_add.eps}}$

``Music 270a: Sinusoids'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).