This page will help you understand how to use Dr. Bongo's Fourier Transform Lab. Additional help can be found on the Entering Functions help page.
Dr. Bongo's Dispersion Lab is designed to help you explore the spectrum of different sounds, and to see how complicated sounds can be "built" from sines and cosines.
Note that all numbers in this program are assumed to be in SI units; units should not be entered into any of the boxes, since it will just confuse the simulation.
The layout of the applet is divided into three columns.
The left column contains input fields which allow you to describe or create the waveform as well as buttons to reset the applet and to recalculate/record the waveform. Each field in the left column is explained below.
|"Reset All" Button: This stops the simulation and resets every parameter to its default value.|
|Waveform: With this dropdown menu you can select to use a "user defined" calculated waveform, to record a waveform with a microphone, to use one of the pre-recorded sounds built into this simulation.|
|User Defined Waveform: f(t): If you select "User Defined Waveform" in the dropdown menu, the computer will use the function you enter into this box to calculate the waveform. The function you type should return values from -1 to 1. The independent variable you should use is t. This variable runs from 0 to about 1.49 seconds. For more information on entering functions into this box, see the Entering Functions page.|
|Recalc/Record: Pressing this button will cause the computer to recalculate the waveform, reload the waveform, or record a new waveform depending on what is selected in the dropdown menu.|
The center column contains two plots. The upper plot is a plot of the waveform in time. The lower plot is the spectrum of frequencies contained in the wave packet. In other words, the wave packet can be considered to be a sum of sine waves, and the lower plot shows the amplitude of each of the sine waves in the sum.
You can zoom into a portion of either plot by simply clicking and dragging to draw a box around the area you want to magnify. Double clicking on the plot will adjust the scaling such that all of the data will be shown. This can also be done by pressing the "Zoom to fit" button in the rightmost column. Right clicking on a graph pane will momentarily display the (x,y) coordinate of the point nearest to the mouse pointer.
The right column contains buttons to zoom the displays and to play the waveform through your computer's speakers. Each button is explained below.
|Zoom to fit: Clicking on this button will set the scales on the two plots to the maximum magnification which still shows all of the data. You can "zoom to fit" each of the plots individually by simply double clicking on the plot itself.|
|Turn on/off Autozoom: When autozoom is turned on, each time the wave changes (i.e., when you select a different prerecorded sound, record a new sound, or change the equation for a calculated sound) the computer will automatically zoom the plot windows to fit the data.|
|Play Wave: Pressing this button will play the waveform through the computer speakers.|
|Turn on/off Autoplay: When autoplay is on, each time the wave changes the new waveform is automatically played through the computer speakers.|