To understand how sound reinforcement systems work, meaning what we call sound reinforcement systems or P.A. (Public Address) systems, we need to recall some basic theoretical concepts. Many sound engineers, perhaps because they have been working in live sound for some time and left their academic studies years behind, no longer remember these concepts, which, although basic, are applied every day in a sound reinforcement job.
Physical Characteristics of Sound:
Frequency: The number of cycles per second is called frequency, and its unit is the hertz (Hz). Our ears can hear between 20 and 20,000 Hz, although this range narrows with age. The lowest frequencies correspond to what we usually call "bass" sounds, that is, slow vibrations, while the highest frequencies correspond to what we call "treble" and are very fast vibrations.
Period: The time (T) needed for an oscillation to repeat. The relationship between period and frequency is: f = 1/T
Wavelength: The distance (l) between two successive points with the same pressure. (l) = v/f = v.t
Amplitude: The maximum value an oscillation reaches in one cycle, also called the "peak value."
Speed of sound: Sound travels at a speed that varies with temperature: the higher the temperature, the faster it goes. In our calculations we will use the speed at 15 ºC, that is, 340 m/s. This comes from applying the formula V = 331 m/s + (0.607 ºC).
Sounds Can Be Pure or Complex
A pure sound, or pure tone, contains a single frequency, but this type of sound is exceptional in nature. A tuning fork produces a pure tone. Complex sounds are made up of multiples of a frequency, for example, the note A (440 Hz). When produced by an instrument, it is made up of the fundamental note and its multiples, which are the harmonics, among others. Its wavelength (l) will be 340/440 = 0.77 m. Given that the speed of sound is 340 m/s, the octave above this note would be exactly double the frequency, 880 Hz, and its wavelength would be exactly half, 0.38 m, so the higher the frequency, the shorter the wavelength, and vice versa.
* Photo: Metallica tour with Meyer Sound systems.
Another major theoretical aspect of sound is the decibel and its relationship to power and intensity.
To represent the dependence of a physical quantity whose value spans a wide range with respect to a variable, we show its dependence on the logarithm of that variable (Log X).
This type of representation is what is called the decibel (dB) scale. The decibel is one tenth of a bel. The bel is the base-10 logarithm of the ratio of two powers or intensities. This unit turns out to be too large, so use of one tenth of a bel has become standard. Decibels are used, for example, for intensity and loudness levels, since the relationship between the two is not linear.
In all cases, it is used to compare one quantity with another called the "reference." Normally, the value taken as the reference is always the smallest value of the quantity.
Example: at a concert, the intensity of an instrument can be 100 times greater in front of the audience than behind it, even though that is not really the impression we get. In practice, when we raise a signal by 3 dB, it is equivalent to a sensation of double the power.
Power and intensity ratios expressed in decibels are:
I = 10log I/Io Io = Iref(*)
DESIGNING A SOUND REINFORCEMENT INSTALLATION
SPL LEVEL
The sound pressure level (SPL) we need is dictated by the ambient noise level of the venue we are going to cover and, from there, the signal-to-noise ratio we want.
In places such as shopping centers and train stations, the SPL is fairly close to the ambient noise level, since the purpose of the sound in these installations is simply to make shopping or waiting more pleasant. If an emergency message needs to be broadcast, the system must be able to reproduce it at least 20 dB above the noise level.
As a general rule, we will try to make our system capable of reproducing 25 dB above the ambient noise. For example, a normal conversation between two people is usually 55 dB, and the audience at a rock concert can reach 80 dB! So our sound system must be able to reach 105 dB. To that we add a peak level of at least 10 dB for speech (rallies, conferences) and 20 dB for music (concerts, clubs).
* Photo: Alejandro Sanz with D.A.S. Audio systems.
SOUND SYSTEM INTELLIGIBILITY
Intelligibility is how clearly a sound message is understood. It can be calculated for a given system.
The SPL ratio between the message and the ambient noise level is decisive for intelligibility. But other parameters also affect intelligibility, such as:
- Signal-to-noise ratio (S/N).
- Reverberation time (RT60).
- Distance from the source.
- Source misalignment.
- Early reflections.
- Late or high-energy reflections.
Alcons Percentage
In 1971, M.A. Peutz published his formula for calculating the loss of articulation of consonants, called the "percentage Alcons":
D2: the distance from the loudspeaker to the farthest listener.
V: the volume of the room in *.
RT60: the reverberation time in seconds.
Q: the directivity factor.
M: the critical distance modifier, usually 1.
N: the ratio between the acoustic power produced by all the loudspeakers and that produced by the loudspeakers providing direct sound to the listener.
If the Alcons percentage is below 10%, intelligibility will be very good; between 10 and 15% it will be good, while above 15% it will be good for simple messages or experienced speakers. The graph below shows the S/N ratio against the Alcons percentage. The percentage improves as the S/N ratio does, up to 25 dB. Beyond that, articulation doesn't improve even if S/N increases.
Reverberation Time (RT60)
We define reverberation time (REV TIME) as the time needed for the level of a signal to drop by 60 dB after the signal has stopped.
Reverberation time is:
V * S / a * S
T = time
V = volume
S = total surface area
* = Constant 0.161
Critical Distance
This is the distance between the source and the listener at which the reverberant energy equals the direct energy. The greater the RT60, the shorter the critical distance.
SYSTEM COVERAGE
This is the uniformity of the SPL across the audience. When designing our system, we should try to get coverage that is as uniform as possible; this means the variation in SPL from one listening position to another should be minimal, to avoid sweet spots on one hand and areas with poor sound quality on the other. We must avoid both subjecting listeners close to the cabinets to excessive SPL and leaving those farthest away without a sufficient, clear level.
Remember that a loudspeaker's coverage is its useful angle, that is, the distance between the two off-axis points where the sound pressure drops by 6 dB.
SYSTEM FREQUENCY RESPONSE
The audio spectrum extends from 20 Hz to 20 kHz, but our system obviously doesn't necessarily need to reproduce this entire frequency range. The range to be reproduced depends on the application. So while a system used for a conference only needs to reproduce from 200 Hz to 6,000 Hz, a club system must cover 50 Hz to 20 kHz.
Choosing loudspeaker systems with a 50 Hz - 20 kHz on-axis frequency response means that in an anechoic chamber (where there is no reflected sound) the system's response doesn't fall more than 10 dB at those frequencies relative to the value given as sensitivity.
* Photo: Alejandro Sanz with D.A.S. Audio. systems.
CHOOSING THE P.A. AND MONITOR SYSTEM
Before choosing the P.A. and monitor system, we need to know the technical requirements imposed by the event (power, frequency response), the artistic ones (number of mics, effects), and the acoustic characteristics (indoor, outdoor). We must know whether the sound field is free, diffuse, reverberant, semi-reverberant, a pressure field, and so on, and know the levels required over the audience area.
INVERSE SQUARE LAW
This law tells us how the SPL changes as we move away from the sound source. The change is 6 dB each time we double the distance.
SPL (measurement distance) = SPL (reference distance) - 20 Log (measurement distance / reference distance)
Atmospheric Absorption
Energy is lost due to the viscosity and heat conduction of the air, along with the rotation of its molecules. The variation in absorption, especially at high frequencies, must not be ignored: imagine a sound check done at 2 p.m. and a show starting after midnight.
The frequency response is also attenuated, especially at high frequencies, due not only to temperature but also to humidity and atmospheric pressure.
Reflection and Absorption
Sound can be reflected when it hits an object larger than a quarter of its wavelength (reflection off the object), whereas when the object is smaller than a quarter of a wavelength there is diffraction (the sound wraps around the object).
P.A. AND MONITOR SYSTEM
We now have practically all the elements to choose our P.A. (Public Address) and monitor systems. The P.A. will be the main sound system for the audience, while the monitors, also called wedges because of their shape, will be the sound system for the musicians: the foldback.
The P.A. and the monitor system are two completely different sound systems, each made up of loudspeakers, power amplifiers, a mixing console, equalizers, dynamics processors, and so on, with a sound engineer for each system, although a single console and engineer can also be used to run both systems.
What we can say up front is that we will need as many monitors as there are musicians, and some may even need more. The monitor console must have as many outputs as monitors are needed. We will also include dynamics processors in our setup for greater control of the signal on stage, graphic equalizers for each monitor, and some effects according to the musician's artistic needs. The console, the effects rack, the dynamics, the equalizers and the monitor engineer should be set up at the side of the stage.
As for the P.A. system, once we know the above, we can choose the dB SPL levels needed for our cabinets and the frequency response required by the type of event being covered. The number of listeners and the size of the venue will determine the power needed and the directivity of the cabinets.
CHOOSING AND PLACING THE CABINETS
Since music will be reproduced and the angle to cover is quite wide, we can try to solve our system with side columns, one on each side of the stage.
Imagine we have cabinets with a sensitivity of 102 dB SPL (1 W/1 m) that handle 1,000 W: What SPL do they deliver at 1 m when we apply full power?
SPL at full power (RMS) = 102 + 10 log (1,000 / 1) = 102 + 10 * 3 = 132 dB
The SPL we will have 60 m from the cabinet along its axis will be:
SPL (at 60 m) = 132 - 20 log (60/1) = 132 - 38 = 96 dB SPL
If we put two cabinets side by side, there would be a risk of overlap, that is, the sound generated by one cabinet would add to the sound generated by the other, so the levels would add, but not across the whole frequency spectrum. Every time we add more cabinets, we get a 3 dB level increase.
The classic way to place the cabinets is on the stage, left and right. If we place more than one cabinet per side, whether side by side or one on top of another, we are talking about "stacks." This arrangement has its advantages and disadvantages: the best thing is how easy and fast it is to set up, and the worst is the attenuation caused by the audience and by distance.
The other option is to place the cabinets on either side of the stage "flown," also called a "cluster," suspended from a structure, which avoids that attenuation by the audience and improves the vertical coverage of the array.
