In some respects the reproduction of low frequency sound is simplified, in others it is harder. But above all, accurate reproduction of low frequencies is possible and it has been done, even if it is not commonplace. Earlier parts of this series have emphasised that the information in audio is primarily carried in the time domain and that time accuracy is essential for realism. Undue emphasis on the frequency domain has led to legacy speakers that are only suitable for certain types of sound, whereas an accurate loudspeaker will be suitable for all audible sounds.

Once the time domain is considered, the events that need to be reproduced are not periodic, but instead are transient. The bandwidth of a step transient is infinite, but as our ears don’t have infinite bandwidth it does no harm if the speaker has a bandwidth limit that is no worse. The point is that for a transient waveform to be correctly reproduced, all of the drive units in the speaker must co-operate in producing components of the spectrum that will add linearly in the air to re-create the original waveform. Clearly such addition can only take place if the signal phase has been preserved. It follows immediately that accurate transient reproduction requires the low frequency unit to have linear phase.

Generation of low frequencies follows from the laws of physics. Sufficient volume velocity must be created by a diaphragm having a suitable combination of area and displacement. Figure.1 shows that the displacement goes up as frequency goes down. There is no way around it: good low frequency reproduction cannot be obtained from very small devices. Low frequency drivers need longer throw than other drive units, but this cannot be taken to extremes. Long throw transducers are not efficient because only a small part of the coil is in the magnet gap. The surround necessary to seal the edge of the diaphragm becomes difficult to engineer with long travel. 

The rolling action of the surround means that in the neutral position about half of the mass of the surround is supported by the chassis and half by the diaphragm. As the diaphragm moves forward from the neutral position, more of the roll surround mass is supported by the chassis. As it moves back, the opposite happens. Effectively the diaphragm has variable mass and this can be a source of distortion.

A drive unit with sufficient volume velocity is not enough. It must be mounted in such a way that the volume velocity results in sound radiation. Low frequency units are always small compared to the wavelength of the sound; this means the volume velocity from the rear of the drive unit will cancel that from the front unless the two are kept separate. That is the purpose of the enclosure; it ensures that the cancellation is prevented.

Traditionally, low frequency reproduction was difficult. Amplifiers of sufficient power were not available or were expensive, high performance magnetic materials were not available and high strength-to weight materials for diaphragms were expensive. As a result, a large number of enclosures were built that tried to improve efficiency or frequency response by trying to use the radiation from the back of the diaphragm as well.

Figure 2a) shows the most popular solution, which is the bass-reflex speaker. Here a short duct is installed in the wall of the enclosure which contains an air mass. The air in the enclosure acts like a spring and the air mass in the duct will resonate with it. The frequency of the resonance will be chosen to augment the response where that from the drive unit is falling.

Figure 2b) shows a variation on the theme which is where the air mass has been replaced by an un-driven diaphragm called an auxiliary bass radiator (ABR) or “drone cone”.

The transmission line speaker in Figure 2c) is another attempt at using the back wave of the drive unit. It is passed down an acoustic delay line until it has been delayed by half a cycle at some frequency.

Figure 2d) shows another variation in which the drive unit is mounted between two chambers and the radiation is entirely from a port. This is known as a band-pass enclosure.

I don’t propose to say a lot about these approaches because the reasons for their development no longer exist and because it should be clear that they are inconsistent with phase linearity. That is why loudspeakers employing these techniques sound like, well, loudspeakers and not like the original sound. By fixating on the frequency response the time accuracy has been damaged.

Nothing makes that clearer than to look at a transmission line speaker in the time domain. The left side of Figure 3 shows that the half cycle delay puts the back wave in phase with the front radiation, which it can augment. Sounds perfect, doesn’t it. Unfortunately there is only one waveform for which a phase shift is the same as an inversion and that is a continuous sine wave. For all other waveforms, the ones that carry information, the transmission line fails and the waveform is comprehensively demolished as the right side of Figure 3 shows.

The approaches illustrated in Figure 2 allows various combinations of smaller amplifiers, smaller enclosures and flimsier drive unit diaphragms to be used. These are all economy measures and as usual, there is no free lunch. Not one of the approaches shown in Figure 2 can hope to recreate the input waveform. All they can reproduce properly is a sine wave. They will fail step response and square wave tests spectacularly and the ostrich-like solution is simply not to publish the results.

If it is hoped to move forward and create accurate active loudspeakers that actually sound like the original sound, it is regrettably necessary to leave all of these passive approaches in the past where they belong and to adopt approaches that actually meet the expectations of the human auditory system using modern materials and technology.

As was mentioned above, in some ways low frequency speaker design is easy. For example, if all of the design techniques that fail to meet psychoacoustic criteria are discarded, then a solution can more readily be chosen from what is left.

The only enclosure the author is aware of that can form the basis of a phase linear loudspeaker is the sealed box in which the only sound radiated is from the outside of the diaphragm. This is not without problems, but they can be overcome. Some of the problems stem from the characteristics of air.

The air in a sealed enclosure obeys the Gas Laws and acts like a spring in parallel with the drive unit’s own suspension. As the enclosure gets smaller, the air spring becomes stiffer and the fundamental resonant frequency of the system rises. Without equalisation, the sound radiation falls off strongly below resonance.

The diaphragm and the enclosed air form a non-linear system. When the diaphragm moves in, the volume it subtracts is a larger proportion of the enclosure volume than the same volume added when it moves out. However, the Gas Laws have another surprise for us. When a gas is compressed, work must be done acting against the pressure and that work results in the temperature rising. If the heat is allowed to escape, then the process is said to be isothermal and the product of pressure P and volume V is constant. However, changing the pressure of a gas at audio frequencies gives it no time for the heat to flow and the process is said to be adiabatic. In that case it is PV^γ that is constant, where γ is the adiabatic index. Figure.4 contrasts isothermal and adiabatic compression.

What this means is that a volume of gas being compressed adiabatically is less linear than if the compression is isothermal.

This is great news for road transport. The temperature rise due to adiabatic compression enables the Diesel engine to obtain ignition with no spark, and the fundamental non-linearity of air springs allow them to be soft to soak up rough roads, but to stiffen up if the vehicle rolls. So it’s an ill wind……….

Some time ago there was a trend to create woofers having very high suspension compliance such that most of the restoring force came from the air spring. It should be clear that these so-called acoustic suspension speakers were prone to distortion.

The apparent volume of a woofer enclosure can be increased by filling it with a suitable porous substance that is in close thermal contact with the air. This converts the compression to isothermal by stabilising the temperature. The density is optimised to obtain the lowest fundamental resonance and that also offers the least distortion.

Sealed enclosures require a distinctive approach to drive unit design. The higher pressures generated require a diaphragm that is very stiff by conventional standards.

Equally, a motor having a high damping factor is required so that the diaphragm is controlled by the amplifier and not the air spring. In an active loudspeaker the fundamental resonance of the driver in the enclosure is not relevant as it can be equalised in frequency and phase very easily. It is often possible to obtain adequate performance with equalisation only, but in some designs motional feedback is used, typically using an accelerometer on the diaphragm. Clearly the feedback will make the accelerometer move accurately, but that is a waste of time unless the diaphragm is stiff enough to follow it, so again a suitable drive unit is required.  

Parts 1 and 2 of this loudspeaker series can be found with the links below.

Loudspeaker Technology: Part 1

Loudspeaker Technology Part 2: The Time Domain and Human Hearing

A complete list of Watkinson’s articles can be found with The Broadcast Bridge search function located on the home page. Simply enter “Watkinson” without the quote marks.

Editor’s note;

John Watkinson has a new book readers may wish to view.

In The Art of Flight, John Watkinson chronicles the disciplines and major technologies that allow heavier-than-air machines to take flight. The book is available from Waterstones Book Store.