of Microprocessors

MUSIC SYNTHESIS PRINCIPLES
19
SIN (A)
(A)
cos (A)
(8)
Fig. 1-4. Mathematical sine wave generator
constant speed. The angle, A, between the crank arm and the centerline of
the crank axis is the angle ofinterest. As the crank turns and time passes, the
angle gets progressively larger. The distance from the center of the handle to
the horizontal centerline of the crank axis, which represents the side opposite
the angle, is the sine of this progressively increasing angle.
Also shown is a graph of the sine as a function of the angle. If the crank
is being turned one revolution per second, then the frequency of the sine
wave on the graph is 1.0 Hz, and the horizontal axis units may be changed
from degrees to time. Ifthe -speed of turning is increased, then the frequency
of the sine wave would also be increased. Sometimes the term "instantaneous
angular velocity" is used when the frequency varies. If rapid variations are
encountered, simply counting the number of complete sine wave cycles in
1 second may not be precise enough. In such cases, angular velocity refers,
conceptually, to the speed of crank turning, which can be measured very
quickly.