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15 augusti, 2011


From one domain to another

At heart of our work at Earo is to design speakers that are suitably impedance matched to the air. Our white paper dives into more detail on this subject than I´ll do in this posting, what I wish to cast some light on is one particular case where poor impedance matching is used to enhance low end performance, the reflex speakers port.

What triggered this posting are remarks from listening session that sound a bit like this;

“ The horns produce less bass bit than my X-brand reflex speakers. But I can hear more detail”

Something causes our perception to say there is more bass.  But what does our perception rely on? I´ll come back to this a little further on.

However, looking in the frequency domain, at the response in level from bass to treble there is a hint of a reply in some cases, in others not. What I am referring to is the temptation to design the reflex mechanism so that it creates a rise just before the low end roll-off. This does create a feeling of deeper bass, but its not. The reflex speaker designer uses the open ended tube to create a resonance at a fundamental frequency where the speaker would begin to roll off. The source of this enhancement comes from the energy inside the cabinet, from the backside of the driver. Thus it is in antiphase to what happens at the front.  In other words, the sound is delayed half a cycle at the frequency where the resonance is defined.

In an open ended tube,as shown in figure above, is often used in bass-reflex speakers. The first resonance occurs at half the wavelength. At every new wavelength, multiple of the fundamental (harmonic) another resonance occurs, so the reflex tube does not only emit sound pressure at one single frequency but at many. So if our reflex speaker designer uses a tube that resonates at 30Hz it will also produce sound at 60, 90, 120Hz, etc.., if those frequencies are produced by the driver unit.

As you can see from the figure, the mouth of the tube is the place where the pressure is at minima and the rate of change is at maxima. This is the high impedance point.

Closer investigation of the tube will reveal that the length of the tube does not exactly match the underlying mathematics. The reason for this is that as energy is put into one end and for it to return to add to the pressure inside the tube it must be reflected back in some way. Just as an Olympic swimmer reaches the end of the first lap and hits the far end of the pool, a turning is required. In a reflection this means the phase is inverted such that the returning reflection is now in-phase with what is going on inside the tube.  The mechanism for reflection is the large impedance step occurring the moment the air exits the tube and finds itself in open air. Exactly where this occurs depends on the diameter of the resonant tube and into what space it radiates.

So, we know from this that what is giving the enhanced bass is slightly delayed. We cant see this in the frequency response because it only shows what is going on in the frequency domain, not the time domain. The time domain is like a third axis, imagine it being the dimension that goes from the paper/screen to your eyes. The time domain gives us information about the duration of a single frequency.

How about our perception then? We know that our perception of loudness (SPL-sound pressure level) is defined as volume per time unit. In plain language as liters per second of air. The first thing about this is that indeed is our perception of loudness connected to the time axis. You could say that our perception of bass is for how long time we are exposed to it, not just the momentary level.

But there is more to it.

Air at normal room temperature has mass. It weighs around 1,2kg´s per cubic meter. Thus the air in the resonant tube will have, a not insignificant, mass. This mass takes time to accelerate into a full blown resonance and once the signal from the driver is gone it will keep on resonating in a decaying fashion.

What you see in the figure above is exactly this, at the initial onset of a transient in the bass, nothing happens.  If the signal is more continuous the reflex port will gradually begin to contribute to what the driver units front side is doing. Once the driver stops nothing happens and then a gradual decay will follow.

From a perception (and energy) point of view, measured over a window of time, more has happened. But is it part of the original musical signal? I´ll let you answer that one.

This now fully explains what is NOT present in the horn but in the bass reflex speaker.  There is even a term for it, “hangover”.  So, next time you get to listen to a horn and a bass reflex speaker using the same material, compare carefully.

One conclusion can be made. Bass reflex speakers create a type of trans-domain distortion at the fundamental and its harmonics. What you gain in quantity you lose in quality.

Another conclusion is that looking at the frequency plot from manufacturer X tells us very little about the speaker unless you also study the time plot. This now becomes rather complex why the best advice is to listen.

Footnote; well designed reflex speakers can apply moderate amounts of resonance and get good sounding results. The smaller the volume in the resonant cavity the less of an issue as it is the mass of air that is the problem. Thus, the problem grows with speaker size.

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