Micah Shepherd and Dr. Timothy Leishman, Physics and Astronomy

After becoming familiar with measurement techniques and equipment, I measured the pressure of the sound field in 5 cm increments between the frequencies of 50 and 1600 Hz inside an impedance tube with a rigid termination. I then analyzed this data and found that the sound field was not uniform and therefore, not ideal for listening. I also calculated the average mean squared pressure in the field. I then used the pressure data to estimate the particle velocity using Euler’s equation and found the total acoustic energy density. I compared these quantities and found that a single energy density measurement was a much better approximation of the average pressure than a single pressure measurement. These values were then inverted and used as a filter to equalize the entire sound field. The average pressure filter would represent the best possible equalization, because it is based on the average pressure response of the entire field. The energy density filter, as expected, made the sound field much more uniform. The equalized sound field was close to but not exactly the same as one using the average pressure filter. The pressure measurement showed that at the location of the microphone, the sound field was very flat, but at all other locations, the sound field was the same or worse as the unequalized field. I then used a parametric equalizer to build an equalization filter based on the three measurements: pressure, energy density, and average pressure. These filters, although not exact, showed good agreement with the ideal filters. This shows that using a parametric equalizer, you can equalize the sound field in the tube much better using a single energy density measurement, than with a single pressure measurement.

I then used a graphic equalizer to create the energy density filter and equalized then sound field. Since the graphic equalizer does not have frequency resolution and variable filter bandwidths, it cannot recreate the ideal filter as well as the parametric equalizer. However, after equalizing the field, the sound field was about the same as the equalized field using the ideal pressure filter. This means that using cheaper equipment and energy density, you can equalize the field as good as or better as using the expensive and precise equipment.

Next, I tested the affect of the termination on the equalization filters. I changed the rigid termination to a anechoic termination and measured the same quantities as before. Again, the energy density and the average pressure were very similar. I then used a semi-absorptive termination and did the same measurements. This showed that the pressure and energy density were similar. This is not what was expected and more tests with be done to confirm this.

In the future, I will be working on using an adaptive filter to equalize the sound field, and testing the effect of the source location. I will also test this method in a room and try to create a technique that can be implemented in sound engineering industry.