Resonant Modes & Sound Cancellation
ASC founder, president and TubeTrap inventor, Art Noxon, PE discusses resonant modes create sound cancellation as published in Home Theater magazine.
The proper placement of subwoofers in your home theater system is crucial to the quality of the desired sound. Placing them in the correct location creates a bass sound level smooth with frequency.
The subwoofer generates very low frequency sounds. The size of these sound waves compares to the size of the listening room. If the subwoofer is placed in the wrong position in the room, we hear “room booms” instead of the musical base scale. On the other hand, if we get the subs into the proper location, the bass sound level becomes smooth with frequency. Subwoofer extension into deep bass is achieved along with significant punch capacity. In this section of work, we will study both the good and bad placement positions for subwoofers located in smaller sized listening rooms, the kind most of us have. Bad speaker positions are those that allow the speaker to stimulate room resonances (modes). Good speaker positions are those from which the speaker cannot stimulate such “room boom” effects. These golden spots are called the anti-mode speaker positions.
To gain some understanding of mode vs. anti-mode speaker positions, it will be very helpful to consider a one-dimensional acoustic space. In a regular room, sound can travel in any direction. If, however, the speaker was located at the end of a long, narrow pipe, the sound could only travel in one direction, along the axis of the pipe. A pipe is a one-dimensional acoustic space. If we plug up both ends of the long pipe, then the “boundary conditions” of a one-dimensional room are met. This is a similar idea to a room having walls.
If the woofer is positioned at one end of the big pipe and a frequency sweep is delivered to it while a sound meter is positioned at the opposite end of the pipe, we will see evidence of the modes. At first, in the very low frequency (LF) range, there are no special changes in the sound level meter. Sooner or later, there will be some frequency where the meter needle gets pegged. The sound got exceedingly loud at this opposite end of the tube, marking the first or “fundamental” resonant frequency and mode.
As the frequency sweep continues upwards, the meter level drops back to normal for awhile, but finally peaks again. This next frequency marks the second resonance mode and is called the first partial or first harmonic. Curiously, the frequency of this second resonance is exactly twice that of the first resonance. We go up some more, only to find another resonance, the third resonance or second partial which is exactly three times the fundamental resonance frequency. This harmonic. series goes on and on with this same pattern.
Needless to say, if we moved the speaker to the opposite end of the pipe, exactly the same harmonic series would be developed. However, if the speaker was moved to the exact middle of the pipe, the first resonance would not sound out. Nor would the third resonance, the fifth, and so on. Odd numbered resonances cannot be stimulated in a closed pipe when the speaker is located in the middle of the pipe. From the middle of the pipe the speaker can only stimulate half of the total number of resonances available to the pipe, the even numbered resonances.
This position-dependent selectivity does not stop with the ends or middle of the pipe. Move the speaker to a position one third from either end and, presto, only the third, sixth, ninth, and so on harmonics can be stimulated. Then we move to a position one quarter of the pipe length from either end and are not surprised to find only the fourth, eighth, twelfth, and so on harmonics. And next the fifth … and so on.
The reason for harmonic selectivity is not in magic numbers, or any other form of audio voodoo. It’s more like simple physics, otherwise known as the nature of things. A playset swing can provide a good example for this effect. As children, most of us learned to “pump the swing” by coordinating our leg/body action with the position, more accurately, the phase of the swing’s position. It’s all in the timing and it is pretty hard to explain, so we teach by showing. Monkey see, monkey do. If we can get the timing right, up we go, almost like magic.
The swing system is a resonant system and a pipe filled with air is also a resonant system. Either can be pumped up by applying the right kind of force at the right place and time. In a closed pipe, which has been stimulated into its first resonance condition, we will find that the sound is very loud at either end of the pipe and very quiet at the halfway point, the middle. These loud areas are called sound “pressure zones”; and, if the speaker is located in either of these pressure zones, it efficiently couples to and can pump up the resonant condition. Conversely, if it is not so located, it can’t pump.
The second harmonic of a closed pipe has three pressure zones, one at either end and one in the middle. If we located the speaker in any three of these pressure zones, we can stimulate the second harmonic. However, if we locate the speaker in the middle pressure zone, we cannot stimulate the first resonance but we can still stimulate the second one. Once the understanding of these variables has been made clear, it becomes easy to expect what will happen if a speaker is located in any particular location.
It seems that no matter where a speaker might be located in a closed pipe, one resonant harmonic series or another will become stimulated. However, subwoofers are always rolled off just below the beginning of the vocal range, about 85 Hz. This means that the subwoofer cannot stimulate resonances above the roll off frequency. Now, if the first resonance is 25 Hz, the second will be 50 Hz, and the third 75 Hz. The fourth resonance will be at 100 Hz. The fourth resonance and all of those higher than it are above the 85 Hz roll off frequency of the subwoofer. This means that the speaker need only be positioned so that it doesn’t stimulate the first, second, or third resonances. The speaker has to be located somewhere, but not at either end, not at the middle, and definitely not at the third way points.
Continue reading this article here and be sure to check out ASC’s SubTrap to smooth out that bass.