Being in one position or another in a concert audience means the sound each listener perceives will be different. This phenomenon is unavoidable and is a consequence, among other things, of interference between sources, which can be constructive, in the case of summation, or destructive, in the case of attenuation. If we look at the frequency response given by an RTA at a concert, we see peaks and valleys.
Unfortunately, the RTA cannot tell us whether these irregularities in the response are caused by differences in arrival time at the measurement microphone or by some defect in the way the loudspeakers reproduce the sound. The only way to find out would be to perform a transfer function with any measurement program that offers this option.
The ear is used to hearing reduced energy in a band (due to sound-absorbing material, for example), so the ear will notice a boost more easily than a cut. In general, a boost of around 6dB is as noticeable as a cut of 9dB. That is why, when mixing, it is preferable to cut unwanted frequencies rather than boost the desired ones; this will give the sound clarity. If we look at the mixing console after a mix done by an experienced engineer, we will find more cut settings than boost settings.
The maximum summation of 6 dB occurs when two signals of equal level combine. This is the most positive aspect of the comb filter. On the other hand, the cancellation effect is extremely deep and wide. The bandwidth of the peaks and valleys is asymmetrical, the former being wider than the latter. While the size of the peaks can be reduced with EQ, the valleys are too deep and wide to be equalized in any practical way.
As the level mismatch increases, the size of the peaks and valleys shrinks and the slope of the filter shapes becomes less severe. This makes the system more amenable to equalization. The progressive narrowing of the percentage bandwidth of each successive peak can range from an octave to hundredths of an octave. For EQ to be effective, the equalizer would need adjustable bandwidth and center frequency.
The equalizer should only be used once the other methods of system alignment (such as repositioning and adjusting delays and levels) have been exhausted; by then, time mismatches will have been minimized and level mismatches maximized.
The remaining "ripple" in the response could be fixed with EQ
That's true; however, comb filtering cannot be corrected with fixed center frequencies and bandwidth components, such as 1/3-octave graphic equalizers. At best, these may have a frequency range where their bandwidth matches the system's response. All the others will be more or less narrow. And then we would need to be lucky for that range to fall on one of the standard ISO center frequencies used by graphic equalizers.
Comb filter
The comb filter effect is calculated as follows: if a signal arrives with a difference “x” expressed in milliseconds (this time is known as the offset), to find the cancellation frequency we must calculate the inverse of the offset, that is, 1/offset, and since a cancellation occurs every half cycle, the first one will occur at half the cancellation frequency.
Let's explain this with a practical example:
If one signal reaches us at 41ms and another at 40ms, the offset, which is the difference, is 1ms. Converting 1 ms to seconds gives 0.001s; the cancellation frequency will then be 1/0.001, that is, 1000Hz.
This means we will have a cancellation every 1000Hz, with the first cancellation at half of those 1000Hz, that is, 500Hz! And the following cancellations at 1500Hz, 2500Hz, 3500Hz, 4500Hz....
If we calculate the impulse response, we see that there are two impulses with a time difference, which in the previous example is 1ms; the first impulse corresponds to the signal that reaches us first, and is therefore higher, and the second impulse to the signal that reaches us later, and therefore has a lower level.
So if we know the difference in travel time between the sources, or can calculate it if we only know the distances ( t = e/v), we will also know the cancellation frequency, that is, how often a cancellation occurs, and consequently where the first cancellation, which occurs at 180º of this frequency, will be.
Beating and other acoustic phenomena
This phenomenon occurs when two sound waves are very close in frequency. They are heard as a single signal, but with a phase shift that varies over time, creating a sensation of changing amplitude. If we consider two frequencies F and F + DF, when they combine they form a resulting wave whose frequency will be F + DF/2.
In mathematical terms, 2cos (F + DF/2) means DF cancellations per second, with the beat frequency oscillating at a frequency DF. So a small variation over time will be noticeable. It does not really represent the smallest detectable change in frequency, but rather a perceived ripple in amplitude, produced by the combination of the two pure tones heard simultaneously.
Let's take the following example: two pure tones of 319Hz and 320Hz will be perceived as a single sound of 319.5Hz. Our ear will be unable to tell them apart, but what we will notice is a beating effect once per second.
Beating is perceived as a periodic change in amplitude, a consequence of the physical combination of the two sounds. They will keep beating until the difference exceeds approximately 10 to 15Hz.
We have just seen that sound perception varies with frequency, but it also varies with sound level: as the level increases, the sensation at high frequencies is greater than at low frequencies.
The same happens with the duration of the signal: sounds lasting less than 1 second are not perceived the same way as sustained sounds. A pure 1KHz tone lasting 0.02s is perceived as a lower-frequency sound.
Acoustic factors
Coupling
This occurs when the time and level mismatch is close to zero. In this case, the signals arrive in phase and can add up to a maximum of 6 dB. This is easier to achieve at low frequencies, where the wavelength is long. So the physical offset between several components does not become too large, and the wavefronts stay in phase. We thus achieve power summation in arrays.
Combining
This occurs when the time mismatch is low and the level mismatch is high. To achieve this, the components must be very close together, but there must be a way to obtain a high level mismatch. This can be done by using directional loudspeaker systems arranged as a point source. This technique is used to widen coverage.
Cancellation
This occurs when the time mismatch is large but the level mismatch is low. It happens when loudspeakers are arranged with identical coverage patterns, such as parallel arrays. While this can give us substantial summation, it is highly position-dependent and causes large variations in frequency response and poor intelligibility.
Echo
This occurs when the time mismatch is large and isolation is low, so that the systems sound like discrete sources. This also causes large variations in frequency response and poor intelligibility, so it must be avoided.
Reverberation
This occurs when there is a large time mismatch and isolation is also large enough that the interaction sounds like a room's normal decay character. If kept to a minimum, it will not drastically affect the system's intelligibility. This is preferable to cancellation or echo.
Isolation
This occurs when the level mismatch is large enough that the second loudspeaker has almost no audible effect on the response of the first. As the time mismatch increases, a greater level mismatch is required to achieve isolation. This is a highly recommended option.
Reflections
Reflections are virtually identical to the interaction between loudspeakers. The cause of summations and cancellations between cabinets is the same as with reflections. A reflective surface can be visualized as a phantom loudspeaker (with another point of origin) that adds energy to the coverage area.
As with the interaction between loudspeakers, reflected energy can be useful. If the time and level mismatch of the reflected energy is very low, we will get coupling. This makes sense; remember subwoofers placed on the floor or in a corner. In this case, the reflected energy doubles or quadruples the loudspeaker's efficiency.
The absorption coefficient of a surface determines the level of reflected sound and the corresponding "ripple." The angle between the loudspeaker, the wall and the listener will have a big effect on its intensity and on the area affected. The more on-axis with the cabinet the reflective surface is, the greater the "ripple."
Let's take the example of an in-line subwoofer array where the spacing between cabinets is less than 2/3 of the wavelength of the highest frequency we are going to reproduce, that is, the crossover frequency. In our example, the spacing between cabinets is 2m.
In the previous case, the sound pressure map holds, since we have not enabled the walls, so there are no virtual sources or reflections. Now we have enabled the wall simulation. We can see that we have constructive and destructive interference in the audience area, which does not affect us that much, because the spacing between cabinets is respected.
Now let's see what happens when we change the distance between the outermost cabinets and the wall. When moving the outer cabinets closer to the wall, we have done it so that this distance is exactly half the spacing between them, that is, 1/6 of the wavelength, in order to take advantage of the phantom source created by the wall.
Another very curious phenomenon occurs with line arrays: the farther we move away from the cabinets, the more constructive or summing interference we get, while as we get closer we get larger differences and therefore destructive interference.
Conclusions
We have seen that there is no clear-cut solution for eliminating the effects of constructive or destructive interference, but we can minimize them. The most immediate solution would be to reposition cabinets and adjust delays and levels; this will minimize time mismatches and maximize level mismatches.
The remaining "ripple" in the response could be fixed with EQ.
