Assignment 1

by

Shridevi kotta

This write up involves the understanding of the function y = a sin(2fx+n). This is a sine wave function. Some of the terms involved in the function have the following terminologies: a is called the amplitude of the wave, n is the phase control parameter and f is frequency control parameter.

A sine function is a periodic function where the values of the function repeat at a regular interval called the period. The period is determined by the frequency factor and is inversely proportional to frequency.

Let’s look at some graphs and see how each of these parameters vary the graph.

First lets look at amplitude. Consider the equation

y = a sin(2fx). In this equation we set f =1. And phase is set to 0. So the period is 2. Y takes on a maximum value = a which we call the amplitude.

The following is some sample waveforms for the given equations with change in amplitude.

When we vary the frequency, we see that period varies inversely proportional. For example we make frequency f =2. Then the period reduces by half to and if we reduce the frequency to 0.5, we see period doubles to 4.

Click here to see the variation in phase: c takes values from –10 to 10.

And also see the graphs below. Phase shifts the graph to right or left. And since it is a periodic function we see that maximum shift we could make is equal to that of the period. Any shift in multiples of period will be the original graph itself.

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