0.11 Jbs2070-a general purpose audiograph program  (Page 6/16)

1. The y value oscillates above and below the horizontal or zero axis much like an ordinary sinusoid.
2. The magnitude of the oscillations builds up with time reaching a maximum near the center of the graph when the sound emitted by each speaker is aboutequal. After that, the magnitude of the oscillations decreases with time.
3. You can hear the zero crossings because a special sound is emitted whenever the function evaluates to zero.
4. If you were to slow the output down to about three pulses per second, you could count the pulses and determine the exact values for x at which thezero crossings occur. (You could probably use this approach to find the roots of Cubic02 and Quadratic01 .)
5. You would learn that the zero crossings occur every eight pulses most of the time for this sinc function.
6. You would learn that there is no zero crossing at an x value of zero. Instead, the maximum value for y occurs for an x value of zero. There aresixteen pulses between zero crossings at the center of the graph.
7. Insofar as zero crossing is concerned, you would learn that the function is symmetric about an x value of zero.
8. If you have a good ear for memorizing a melody, you would learn that the function is symmetric about zero. The values for y on thepositive side of zero are a mirror image of the values for y on the negative side of zero.

Contents of the output file named Sinc01.txt

Listing 6 shows the output data values for this sinc function. (Note that the actual output from the program is a single long string. I manually inserted linebreaks every eight values to force the material to fit in this narrow presentation format. That also matches up with the zero crossings mentionedabove.)

If you examine this data, you will see that it supports the conclusions that were reached above based solely on the audio. For example, the first value on every line exceptthe eleventh line is either 0.0 or -0.0. On that line, the first value is 1.571, which is the largest value in the entire set of values. That value occurs at the center ofthe set of values and matches the peak frequency in the audio.

The values on both sides of that value are 1.531. This suggests that the symmetry conclusion reached above is probably correct. Further comparison of the corresponding values will confirm the symmetry andmirror image conclusion reached above .