The plot of a complex sound wave is the plot of a special kind of mathematical function. It's a type of function that can be exactly represented by the summation of different sine and cosine functions. This is called its Fourier Representation. Synthesizers use Fourier Representation to great affect. They don't produce sounds like individual instruments do; instead they produce the combination of pure tones needed to mimic the instruments.

Once you have the Fourier Representation of a sound wave, you can create another very useful plot-that of its Fourier Transform. This would be a plot of the decibel levels needed at each frequency to reproduce the sound. In the introduction to this series of articles, I mentioned that at the heart of the sound system I was learning is the Yamaha DM 1000 Digital Mixer. I was somewhat surprised that this system doesn't have the ability to perform discrete Fast Fourier Transforms. It sure would make EQ'ing a lot easier.

What Do You Hear?

The table below lists frequencies for some common musical elements (and some other things). It also lists their wavelengths. I often find the wavelength to be the more useful number when trying to understand how a sound will "play" in a room but of course frequency is more useful when hunting an annoying sound during EQing.

"Loudness" is the result of an almost instantaneous difference in pressure that impacts the eardrum. (Relatively slow changes in pressure, like when we travel up a mountain, have no affect because our sinuous systems work to equalize pressure on both sides of our eardrums.) The governing equation is:

The Environment

One of the first mistakes I made when mixing a live show was to rely on the dB meters to balance the channels. What I didn't realize was that the size and shape of our heads, the placement of our ears and the structure of our ear canals all conspire to selectively amplify a certain range of frequencies. Below is a plot of average frequency sensitivity. Notice that our maximum sensitivity is at about 2k-3k Hz.

Reflection: There is a degree to which sound waves reflect from surfaces. They reflect better off some surfaces than others and in fact certain frequencies will reflect off a surface that absorbs other frequencies but, as a rule the softer the surface the less the reflection. In most cases you would like to minimize sound reflection as much as possible.

Venues with concrete floors and brick walls will tend to sound like echo chambers. Ones with carpeted floors and wood or textured walls will have a better sound. Also, it's easier to reduce sound reflection from directional instruments like horns, guitars and vocals than it is from drums or even piano. We use a shield around the drummer but even that doesn't totally eliminate the problem.

Each venue will also be susceptible to a specific frequency of standing wave. This occurs when a wave front reflects off the back wall and constructively interferes with the rest of the wave. This is usually more of a problem in small venues. The offending wavelength is easily identified if you know the length of the room.

Refraction: Previously I spoke about constructive and destructive interference. Well those are aspects of refraction. If you have ever seen a wave tank in a high school science class you'll understand what I mean (boy, you really had to pay attention in high school to get much out of this article). In one experiment they generated some waves and sent them through a couple of small slits. After the waves passed through the slits, becoming two wave fronts, they fanned out and interfered with each other. In another experiment they would place different size objects in the wave path. If the object was large relative to the wavelength you would see a lot of the wave reflected. But if the object was small there wouldn't be any noticeable break in the wave front. Sound waves react the same way; they'll interfere with each other and long wavelength sounds will not be impeded by small objects in the wave path while short wavelength sounds will be reflected.

One of the effects of refraction can be heard if you've ever in the parking lot of a football stadium when the band is playing. Because of the bass drum's long wavelength it will clearly be heard from the parking lot but you won't pick up the higher pitched instruments until your inside the stadium and have a direct line of sight to them.

Dampening: This is a decrease in the amplitude of sound waves-a reduction in loudness. I touched on dampening in the section on reflection when I spoke of surfaces absorbing sound waves-it is hard to separate these concepts. Sound waves also dampen as a natural process of propagation through air--as a portion of their mechanical energy is constantly being converted into heat energy. There is also a non-energy related reason why sound "gets quieter" further from its source. Sound wave fronts spread out in an arc from their source as such someone standing close will experience a larger percent of the wave front than someone standing further back.

Some Observations From A Sound Rookie

The board mix isn't and shouldn't be the room mix. We've put together a system that allows us to broadcast live shows in real time over our web site from any remote location. When we first did this, I thought it would be best to take the signal direct from the venue's mixer. I've found that that's not a good idea, especially if there's a lot of horns, drums or piano in the mix. The reason is that a good sound engineer will be aware of and account for the sound coming off the stage, not just what's coming out of the speakers.

Stereo is usually not a good thing. When mixing for a venue you want everyone in the place to hear the same thing, as much as possible. If the mix is separated you'll only be catering to those lucky enough to be standing in the center of the room.

Bodies absorb sound. This is an easy one. Bodies will change the acoustics of a room, so the mix for an empty room will be different than a mix for a full room. But of course if the room's empty, who cares?

No matter how good you are, you won't be able to cover the room perfectly. It just can't happen. There will always be some quiet spots or even dead spots somewhere in the room or some areas, usually close to the stage, where the mix isn't even.