Sebastijan Skoko
MSI Lieb
10-28-14
Unit 3 - Sounds Good: Moving the Sine Function

The basic element of the sine function is the equation y=sin x, however, by adding additional variables to the equation it can become more complex. In the equation y = asin(b(x-c))+d, the additional values a, b, c, and d, add additional information, changing the curve. 

The value of a changes the amplitude. The amplitude as represented through this curve, dictates how the height of the waves. When the value of a is increased, the waves become taller in height. For example, when the curve is in the middle of the graph (d set to 0) and the value of a is 10, the top and bottom of the waves are at 10 and -10, respectively. To relate to the current unit on sound, a loud sound would have a taller wave and a softer sound would have a shorter wave. 

The value of b changes the frequency. The frequency as represented through this curve, dictates how many waves there are and how often they occur and restart. The more frequent the waves are, the shorter in length they are. When the value is high, or very low (negative) for frequency, the wave lengths are very short and the period (c) is very short. The closer to 0, however, the longer the wave lengths are (at 0 it is a linear function). 

The value of c changes the period. The period as represented through this curve, dictates how long the time between frequencies is. While frequency represents how often, period represents how long as stated by Chris Knight in class. By increasing the value of c, the entire graph moves to the right. Similarly when decreased, the entire graph moves to the left. 

The value of d changes the original height of the curve. By increasing the value for d, the graph slides up without changing it's shape, while decreasing the value for d slides the graph down without changing the shape.