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Fundamental Acoustics Foundations

Sep 23, 2013 4:31 PM, By Bob McCarthy

The facts and fictions of modern audio engineering.

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The first-ever AES Conference on Audio Education was held in July at Middle Tennessee State University (MTSU) in Murfreesboro, Tenn. This led me to reflect on the current state of audio education and what subjects are important to emerging audio engineers. They are certainly not the same topics that were relevant and/or available to me when I created a custom degree in audio engineering at Indiana University in the late 1970s. Current students will not prioritize vacuum tube circuit design, Thiele and Small parameters, magnetic tape editing, transformers, and optical sound tracks as highly as we did in those days. The laws of physics that we studied back then have not been updated, but virtually everything else has.

An education regimen sets a foundation and as a result there is always an emphasis on the timeless aspects of the field: fundamentals, signal paths, laws of physics, and acoustics. Teachers feel the need to cover this stuff instead of getting right to how to mix a festival for 50,000 people. Sadly, we know that we have to get through all of that boring stuff to improve our chances of getting behind the big desk for the big show.

The nice thing about learning the fundamentals is that they stay learned. They also help speed up the process of learning all of the interesting and fast-changing stuff because a solid foundation is better to build on than one full of holes or misconceptions. It will be easier to keep up with industry progress when you have a firm understanding of the things that won’t progress. Think of it like a game plan with 50 percent of your energy spent on the unchangeable, 50 percent on the current industry practices, and 10 percent on past and future directions of our trade. It takes at least 110-percent effort to get that cherry job.

Education is a serious business, but that does not mean we can’t have some fun with fundamentals in the short space we have here. In recognition of AES’ three-day event, here is a dartboard of interesting tidbits that might inspire you to check your audio fundamentals foundation.

Figure 1: Comparison of the log and linear frequency axes (from question 1). Click here to see a larger image.

1. Did you know that the log frequency axis (octaves) is all in your head? The physical world doesn’t sing that song. Physics uses only the linear frequency axis. Harmonics are linear multiples (not successive doublings like log would be). Peaks and dips caused by reflections or multiple speaker interaction are all linear. We need to be linear log bilingual since the acoustical interactions of the world (and most of their solutions) are linear but we experience them with our log hearing. Comb-filter interaction is a perfect example of this. In the linear world, the peaks and dips are equally spaced. To our ears, they get narrower and narrower as frequency rises.

2. Did you know that there is nothing in acoustics that can make a pattern of equally spaced 1/3-octave-wide peaks and dips? Do you think we should tell the makers of graphic equalizers about this?

3. Everything to do with phase affects the frequency response linearly. Phase is about time. There is no logarithmic time, only linear. Tick-tick-tick-tick-tick, not tick--------tick----tick--tick-tick. We should be grateful for this since log time would mean that childhood goes really slowly and then time passes more quickly as we get older. It already seems enough like that already, eh?

Figure 2: The spectral variance progression for a single speaker. Notice that the on-axis far and off-axis near responses are matched, connected by the minimum variance line (from questions 4 and 5). Click here to see a larger image.

4. The inverse square law is just like a traffic law. It is never obeyed. Hypothetically, the SPL drops 6dB per doubling distance but two things screw it up: air and Earth. The air causes extra loss in the HF, especially in a desert. The Earth decreases the loss rate in the low end because the reflection is added to the direct sound path. You can get rid of the Earth bounce by getting the PA really high. That part is easy. But if the audience is near the ground they will still get a strong reflection. So the audience needs to get high also, but that relates to a different law than inverse square.

5. Did you know that if the on-axis response of a speaker is flat at 50ft. it won’t be flat at 100ft.? It will have a tilted response with the low end above the midrange and the high end below. The longer on-axis response gets more air loss and more room reflections, both of which tilt the response. The off-axis near response has less air and less room but gets tilted by the directionality of the speaker. So two places that are likely to have similar frequency responses are on-axis far and off-axis near. You might want to factor this into your speaker aiming.

6. Did you know that you can reduce the need for equalization by having great speaker positions? On the other hand, you can’t reduce the need for great speaker locations by equalization. As they say in real estate: location, location, location. Did you know that putting an I-beam in front of a high-frequency loudspeaker reflects and blocks the sound? If not, you are qualified to be an architect or scenic designer.

7. Have you heard the one about how you can’t measure subwoofers in the near field because the low frequencies have not developed yet? If you would like to test that theory, I invite you to put your ear against the grill of my subwoofer and tell me if the full-power kick drum seems developed enough.

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