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# Acoustical Measurements - Energy-Time Curves and Waterfall Plots

By rives

These can be very useful, although they can be more difficult to interpret as they are a steady state measurement at different times averaged for the entire frequency range, or a band of frequencies. So why would this be important? Well, like the reverberation times, we would like the energy at the frequencies to decay uniformly.

As stated above, one of the problems with energy time curves is that they can be difficult to interpret. Each curve is a very fast snap shot of what energy is present at that time. Because there may be comb filtering at that instance, it can sometimes be deceiving, but it's best to interpret the energy time curves by ignoring any dips in energy that rise again. The following graph shows energy time curves for the full range and the band from 4k to 8k. Notice that they track each other nicely. This is what is expected and is ideal:

A subset of energy time curves is the cumulative decay plots. This is taken across the entire frequency range and is a snapshot at that particular time. The first is at 0 ms, and the subsequent snapshots can be at various intervals depending on what we are looking for. Ideally the 0 ms should be flat (it will have significant fluctuations due to comb filtering, but overall should be flat). If it's not flat, this generally means there is a problem with the equipment, because the direct wave response has no room interaction. This can be a great tool for troubleshooting. I was once sent a set of graphs that showed the cumulative decay at 0 ms (meaning the direct wave), where the frequency response was quite rolled off in the high end. The decay in the high end was not as rapid as everywhere else. The overall (meaning integrated for a long time) frequency response was pretty flat. I called the user and asked him if he had a treble control, he replied he did. I asked if it was turned all the way down-he responded yes. It turned out his room was very reflective with a lot of glass. The glass was leaking bass energy and reflecting the high frequency energy. He compensated for this "brightness", by turning the treble (tweeter in this case) all the way down.

Below is a different graph. One where the energy in the room is falling off rapidly at the high frequencies where the initial (0 ms) response was close to flat.

Waterfall Plots
Eye candy? People have said this to me-waterfall plots are simply eye candy. I firmly disagree. Waterfall plots do look great, but they are very useful. In a simple 3-D snapshot we can see if everything is decaying uniformly. This is basically looking at the cumulative decay in different way. I like it because if I see one particular frequency that is being carried out much longer than all the others, I know it's a resonance of some sort-usually caused by the room. How long it's carried out has a lot to do with how significant that resonance is.

The graph below shows a prominent resonance frequency around 80 Hz:

Psycho-Acoustical Response Curve
This is a highly debated subject, and some might say controversial subject, but in our tests it has proven extremely useful. Some acousticians will say that the steady state response is all that you need and for trained acousticians, who may deal with this on a regular basis, this may well be the case. The basic premise of a psycho acoustical response curve is that it mimics in a 2-D graph what the human ear perceives relative to frequency response. Thus if there is a resonant mode it will be displayed as a peak at that frequency. The human ear has longer integration times at lower frequencies than at higher frequencies. Thus the gate time for the psycho-acoustical response curve is longer for low frequencies than high frequencies. Here is a psycho-acoustical response curve of the waterfall plot seen above.

We use the psycho-acoustical response curve to set up the PARC. It is very easy to interpret and our results have worked out incredibly well by simply using the psycho-acoustical as our benchmark and bringing it's response as close to flat as is possible.

Special Note Regarding the Graphs
All measurements were taken using the Rives Audio Professional Test Kit. The analysis and display software is ETF from Acoustisoft. We have found this software and hardware to be the most cost effective method of obtaining state of the art measurements.

by Richard Rives Bird of Rives Audio

Resources and education in Acoustics: www.rivesaudio.com/educate

Contact Rives Audio: [email protected] or 800-959-6553