![]() ![]() moves a distance \(2\pi f\) per second), then in Cartesian coordinates, the position at time \(t\) is given by If our point starts at \((1,0)\) at time \(t=0\) and moves at a speed of \(f\) full cycles of the circle per time unit (i.e. We assume our circle has a radius of 1 unit, making the circumference \(2\pi\). Assuming that the point has moved by an angle \(\theta\) from the point \((1,0)\) on the \(x\)-axis, we call its \(y\)-coordinate the sine of the angle \(\theta\), denoted by \(\sin(\theta)\) and we call its \(x\)-coordinate the cosine of \(\theta\), denoted by \(\cos(\theta).\) The result is shown in the bottom portion of the figure. At each moment in time, the Cartesian coordinates \((x,y)\) of the point can be recorded, and we can plot either the \(x\) or \(y\) coordinate as a function of time. This quantity is referred to as the sinusoid’s frequency. The speed at which the point rotates about the orign can be measured in terms of the number of complete cycles made per second. Imagine a point moving counter-clockwise around the unit circle at a constant speed. Here \(A\) describes the sinusoid’s amplitude which corresponds to volume, \(f\) defines its frequency, which defines its pitch, and \(\phi\) defines its phase, that is, where in a cycle, as a fraction of the whole circle, the sinusoid starts at time \(t=0.\)Ī sinusoid can be thought of in geometrical terms as follows. So it is essential to understand these key building blocks and how they combine to form complex sounds.Ī sinusoid has a specific functional form that is described using the trigonometric cosine function, and we can write the most general sinusoid as the function You need an iframes capable browser to view this content.Despite the fact that the sound associated with a sinusoid is not terribly pleasant to listen to, one can use such signals as basic building blocks for some truly interesting forms of sound. DJ Val the Vandle has coined himself, The Tastemaker of LA, since earning the stripes of a trendsetter in the LA music scene. He has toured with the likes of Snoop Dogg, Talib Kweli, Drake,
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