From figure 3 it can be seen that the waveform is not a smooth sink function. The theoretical signal showed as red signal move away from the max amplitude the waveform should be decaying. There is still some error present between experimental and calculated signal. There can be multiple reasons for this such as noise, DSA, or simply the nature of the function.

To understand delay in sound travel we attempt the next exercise using DSP and time delay was set up as 10 ms. the code shows the program to convert data from spectrum analyzer to the Matlab and display as a plot.

The slope of the line in plot above represents the sound travel. As it shows in the figure 5 that the distance was increasing as the time increased. This means the further we move the speaker the longer time it take for the sound to reach the speaker. As we know, sound travel 13503.9 inch per second and using this condition we can find the experimental error from the slop of our plot.

The result we obtained for test 1,2 and 3 during the lab containes almost 95 percent errors, which is was not expected. although the plot in figure 5,6 and 7, shows the time delay was increasing as the distance increased. The atmosphere inside the labroom present many different noises, if the experiment was done in a quit room, then we could have got a better result with less error.

All the sound sources measured the same delay as it shows in the figure 5, 6 and 7. The sin wave of 2 KHz plot shows a little different plotting. The result indicate unreliable measurements. As we know, sound waves exist as variations of pressure in a medium such as air. They are created by the vibration of an object, which causes the air surrounding it to vibrate. Since the surrounding contains various sound sources and this might have affected the end result for this experiment

The results in autocorrelation and cross correlation is equivalence between mathematical and actual. The minor error was expected, therefore it can be negligible. During the time delay exercise we observed the difference between the actual time and the experimental time is only 0.68 ms and this is small error due to noise or the digital spectrum analyzer itself. The speed of sound calculated due to the positioning of the microphone contained a big percent of error although the errors are predictable.