B&O Tech: A day in the life

#17 in a series of articles about the technology behind Bang & Olufsen loudspeakers

 

This week, instead of talking about what is inside the loudspeakers, let’s talk about what I listen for when sound is coming out of them. Specifically, let’s talk about one spatial aspect of the mix – where instruments and voices are located in two-dimensional space. (This will be a short posting this week, because it includes homework…)

Step 1: Go out and buy a copy of Jennifer Warnes’s album called “Famous Blue Raincoat: The Songs of Leonard Cohen” and play track 2 – “Bird on a Wire”.

Step 2: Close your eyes and really concentrate on where the various voices and instruments are located in space relative to your loudspeakers. If you hear what I hear, you’ll hear something like what I’ve tried to represent on the map shown in the figure below.

A map of the locations of many of the instruments in Jennifer Warnes's recording of "Bird on a Wire".
A map of the locations of many of the instruments in Jennifer Warnes’s recording of “Bird on a Wire”.

I’ve used some colour coding, just to help keep things straight:

  • Voices are in Red
  • Drums are in blue
  • Metallic instruments (including cymbals) are in green
  • Bass is gray
  • Synth and Saxophone are in purple

Note that Jennifer sings her own backup vocals, so the “voice”, and the two “bk” (for backup – not Burger King) positions are all her. It also sounds like she’s singing in the “choir” on the left – but it’s hard for me to hear exactly where she is.

Whenever I’m listening to a pair of loudspeakers (or a car audio system, or the behaviour of an upmix algorithm) to determine the spatial properties, I use this map (which I normally keep in my head – not on paper…) to determine how things are behaving. The two big questions I’m trying to answer when considering a map like this revolve around the loudspeakers’ ability to deliver the (1) accuracy and (2) the precision I’m looking for. (Although many marketing claims will use these words interchangeably, they do not mean the same thing.)

The question of accuracy is one of whether the instruments are located in the correct places, both in terms of left and right, but also in terms of distance. For example, the tune starts with a hit on the centre tom-tom, followed immediately by the bigger tom-tom on the left of the mix. If I have to point at that second, deeper-pitched tom-tom – which direction am I pointing in? Is it far enough left-of-centre, but not hard over in the left loudspeaker? (This will be determined by how well the loudspeakers’ signals are matched at the listening position, as well as the location of the listening position.) Secondly, how far away does it sound, relative to other sound sources in the mix? (This will be influenced primarily by the mix itself.) Finally,  how far away does it sound from the listening position in the room? (This will be influenced not only by the mix, but by the directivity of the loudspeakers and the strength of sidewall reflections in the listening room. I talked about that in another blog posting once-upon-a-time.)

The question of precision can be thought of as a question of the size of the image. Is it a pin-point in space (both left/right and in distance)? Or is a cloud – a fuzzy location with indistinct edges? Typically, this characteristic is determined by the mix (for example, whether the panning was done using amplitude or delay differences between the two audio channels), but also by the loudspeaker matching across the frequency range and their directivity. For example, one of the experiments that we did here at B&O some years ago showed that a difference as small as 3 degrees in the phase response matching of a pair of loudspeakers could cause a centrally-located phantom image to lose precision and start to become fuzzy.

Some things I’ve left out of this map:

  • The locations of the individual voices in the “choir”
  • Extra cowbells at around 2:20
  • L/R panned cabasa (or shaker?) at about 2:59
  • Reveberation

Some additional notes:

  • The triangles on the right side happen around 2:12 in the tune. The ones on the left come in much earlier in the track.
  • The “synth-y fx around 2:20” might be a guitar with a weird modulation on it. I don’t want to get into an argument about exactly what instrument this is.
  • I’ve only identified the location of the bass in the choir. There are other singers, of course…

You might note that I used the term “two-dimensional space” in the beginning of this posting. In my head, the two dimensions are (1) angle to the source and (2) distance to the source. I don’t think in X-Y cartesian terms, but Polar terms.

An important thing to mention before I wrap up is that this aspect of a loudspeaker’s performance (accuracy and precision of phantom imaging) is only one quality of many. Of course, if you’re not sitting in the sweet spot, none of this can be heard, so it doesn’t matter. Also, if your loudspeakers are not positioned “correctly”  (±30 degrees of centre and equidistant from the listening position) then none of this can be heard, so it doesn’t matter. And so on and so on. The point I’m trying to make here is that phantom image representation is only one of the many things to listen for, not only in a recording but also when evaluating loudspeakers.

 

B&O Tech: Ribs and Dogbones

#16 in a series of articles about the technology behind Bang & Olufsen loudspeakers

 

Take a balloon and blow it up. It will look something like the drawing in the centre of Figure 1.

A balloon in its natural state (the middle), the same balloon being squished (on the left), and the same balloon being stretched (on the right).
Fig 1. A balloon in its natural state (the middle), the same balloon being squished (on the left), and the same balloon being stretched (on the right).

 

If you put your hands on the top and bottom of the ballon and compress them, you’ll make the balloon shorter, but you’ll also make it wider (as is shown on the left side of Figure 1). This is because the air inside the balloon is under a higher pressure when you squeeze your hands together, and that pressure pushes harder on the parts of the balloon that aren’t being held in by your hands.

If, instead, you grab the top and bottom of the balloon and stretch them further apart, you’ll make the balloon narrower (as is shown on the right side of Figure 1). This is because you’ve created more space inside the balloon, thus lowering the internal pressure pushing out on its walls. The lower the pressure, the less the air pushes outwards, so the balloon collapses.

What we’ve described here is basically the same as what happens to a sealed loudspeaker cabinet (if you’re not careful when you do its mechanical design). However, instead of your hands squeezing a balloon (a sealed “cabinet” of air), we use the signal from a power amplifier to pull the woofer into the cabinet. This increases the pressure inside the cabinet, since it’s sealed and there’s nowhere for the air to go. As a result, the trapped air tries to push outwards on the sides of the cabinet. If the walls of the cabinet are thin, then the cabinet itself will act like the balloon and expand.

Similarly, if you put a positive signal on the power amplifier, you’ll move the woofer out of the cabinet, reducing the air pressure inside it and “sucking” the sidewalls of the loudspeaker in (if they are so thin that they can move).

Generally speaking, you want a loudspeaker to behave as a piston in a baffle (like this). This means (in this case) that you want the woofer to move in and out of a loudspeaker cabinet and you don’t want the cabinet itself to move at all. (We’ll talk later about why this is a bad thing.)

There are a number of different ways to do this. One way is to make your loudspeaker cabinet out of something very, very, very stiff (and probably, as a result, very, very, very heavy). For example, we make our prototypes out of 22 mm or 25 mm thick MDF (and sometimes we use two sheets of it, glued back to back, to make sure that things are stiff enough).  Most of our loudspeakers like the BeoLab 9, for this week’s example, have enclosures that are made of plastic, so we use some different methods to achieve the stiffness and rigidity we need to ensure that our enclosures are not singing along with the drivers.

A "naked" BeoLab 9 with the Acoustic Lens assembly removed.
Fig 2. A “naked” BeoLab 9 with the Acoustic Lens assembly removed.

 

The first step in ensuring that the walls of the loudspeaker cabinet are stiff enough is to make them thick enough. How thick is “enough” depends on the loudspeaker itself. A subwoofer with a small enclosure volume will have to withstand more internal air pressure than a midrange in a larger enclosure. Of course, we can’t simply make the walls of the cabinet out of overly thick plastic, since that would not only be an unnecessary waste of materials, it would increase the weight of the loudspeaker (a consideration for shipping) and the cooling time of the plastic when it’s in production (a consideration for the production line timing and costs). 

A second way to make the sidewalls stiffer is to use ribs – usually on the inside of the cabinet. These are moulded as part of the sidewall itself – they aren’t just glued on to the inside surface of the cabinet. If you take a look at Figure 3, you can see the ribs on the inside of the sidewalls of the BeoLab 9. These run diagonally and vertically in the case of this loudspeaker – but they’re not just randomly placed inside the loudspeaker. They have been strategically placed using simulations in the early development stages, and measurements of the early prototypes. These measurements are done using very small accelerometers glued to the sides of the loudspeakers and monitoring their outputs while playing signals through the loudspeaker drivers. (In case you’re wondering, the depth of the ribs is about 22 – 25 mm, depending on where you measure.)

 

A closeup of the ribs on the inside of the woofer enclosure of the BeoLab 9.
Fig 3. A closeup of the ribs on the inside of the woofer enclosure of the BeoLab 9.

 

A third tactic is to use a plastic that is stiffened by adding things to it. The usual method is to use fibre-reinforced plastic. The fibres in the plastic help give it a structural strength that you can’t get from just plastic alone.

A fourth possibility is to create a laminate material where you build up the enclosure using layers of different materials (or layers of the same material with different structural composition). This increases stiffness in the same way that a sheet of plywood is stiffer than a sheet of wood.

So, in the case of the BeoLab 9 (as with many of our other loudspeakers), three of these tactics were used. The plastic is thick enough, it has strengthening ribs on the inside, and it is a laminate (if you slice it open, you’ll see that it is a layer of foamed plastic, sandwiched between “skin” layers of solid plastic).

However, when they (I wasn’t part of the BeoLab 9 development team – I was still working in the Automotive Department at the time) got to the last stages of the development, it became obvious that there was a problem. There was an audible resonance caused by the woofer. Some digging around resulted in the finding out that the sides of the cabinet were moving too much. In essence, the problem was almost exactly as I described with the balloon in Figure 1.

 

The movement of a BeoLab 9 prototype before the problem was fixed.
Fig 4. A not-to-scale cross section of a BeoLab 9 prototype showing a simplified explanation of its “ballooning” effect before the problem was fixed.

 

As I tried to show in Figure 4, when the woofer moved inwards, it pushed the sidewalls of the loudspeaker outwards (shown with the blue lines). When the woofer moved outwards, it sucked the sidewalls inwards (the red lines). (I’m over-simplifying here, but not enough to start a fight.)

However, as I said, this was discovered rather late in the development process. The problem had to be fixed, but the question was how to do it without starting from scratch and creating new moulding tools for making the plastic enclosure. The solution was to use the sidewalls to reinforce each other. Since the movement of the opposite sides was in opposite directions (i.e. the left and right sides of the loudspeaker either wanted to move apart or together at any given moment) they could be braced by connecting them with a bridge. Take a look again at Figure 3. You’ll see a metal rod that goes straight across the middle of the woofer enclosure. You can see it just above the back of the woofer in Figure 5 as well.

 

A view into the woofer cabinet of the BeoLab 9.
Fig 5. A view into the woofer cabinet of a late-stage prototype BeoLab 9.

 

That piece became known in the acoustics department as the “dog bone” because its final version had the basic shape of a cartoon dog bone. The end result is that the rod is included in the BeoLab 9 construction to prevent the sidewalls of the woofer cabinet from moving when you’re playing loudly.

Here’s another photo showing the internal PCB with the amplifier and filters – not because it’s relevant to this discussion, but just because it might be interesting…

 

The electronics (analogue filters and amplifiers) of a BeoLab 9. As you can see here, this circuit board normally lives inside the woofer enclosure. The power supply board is not shown in this photo.
Fig 6. The electronics (analogue filters and amplifiers) of a BeoLab 9. As you can see here, this circuit board normally lives inside the woofer enclosure. The power supply board is not shown in this photo.

 

How is a loudspeaker cabinet like a nude ballet? (Or: so what?)

 

So, we’ve seen how we get rid of parts of the loudspeaker moving when they shouldn’t. The question is “why is it a big deal?” Well, it’s a little like Sir Robert Helpmann’s comment about the difficulties in choreographing a nude ballet – the problem is that some parts of the body keep moving when the other parts have stopped.

In theory, a loudspeaker should behave the same at all frequencies (that statement can mean a lot of different things – and I am happy to argue that it is both true and false, depending. So don’t try to start a fight with me on that one, and please don’t mis-quote me and say that I’m contradicting Siegfried Linkwitz or anyone else by taking that statement out of context on a hi-fi forum somewhere else…) As I mentioned in a previous posting, we like to pretend that a loudspeaker is just a moving piston in an infinite baffle, since that behaves pretty well. Of course, no one actually believes that this model is true – but it’s a comforting ideal.

Take a look at the shape of the blue and red versions of the loudspeaker cross-section in Figure 4, above. You might notice that, when the woofer goes outwards, the cabinet goes inwards. When the woofer goes inwards, the cabinet goes outwards. (this is an oversimplification of the truth, but let’s go with it for now). This means that, from the point of view of the air pressure radiating from the entire loudspeaker, the woofer goes positive and the cabinet goes negative at the same time. So, the sound pressure radiating off the cabinet cancels the sound pressure radiating off the woofer as can be seen in an example of two opposite-polarity sources causing destructive interference as in the animation below. (Note the intersection of the red and green curves where you will hear no sound at all…)

Not only that, but the cabinet as a sound source has a very different directivity than the woofer by itself. So, the result is… complicated. The truth is even more complicated, since the cabinet will not behave as nicely as this – it will resonate better at some frequencies than others, making some notes “bloom” – they’ll appear to be louder (or quieter, depending on where you are and how the room interacts with the loudspeaker) and they might even appear to come from a different direction.

So, the moral of the story here is that you want all parts of the loudspeaker to not be moving when the parts that are supposed to be moving are doing so.

And, before you go and listen to your loudspeakers and look for “blooming” and blaming it on panel resonances or vibrating cabinets, don’t forget that your room modes are more likely a primary source of mis-behaviour when it comes to some bass notes sounding different from the others. However, if you have problems with your room acoustics, we can’t fix that with ribs and dogbones – unless you also bring in a large dog. (I know, I know – the linked paper is about humans – but it does make a mention of animals in the abstract…)

 

 

 

B&O Tech: Curves are Better than Corners

#15 in a series of articles about the technology behind Bang & Olufsen loudspeakers

 

Interference

Before we start talking about curves and corners, let’s have a quick review on the concept of interference. At its most fundamental level, sound is just a relatively small, relatively fast change in barometric pressure. If the instantaneous pressure is higher than average (which happens to be the same as the pressure inside your head), then your eardrum is pushed into your head. If the instantaneous pressure is lower than average, then your eardrum is pulled out of your head. When your eardrum moves in and out, you hear sound.

One way to create a high pressure is to take a loudspeaker driver and push it outwards. In order to create a low pressure, we pull it inwards, as is shown in the animation below. The red thing is a piston which is basically the way we like to pretend a loudspeaker driver (like a tweeter) behaves. The grey thing is a very, very wide loudspeaker cabinet. The red semicircles show the high pressure zones that expand outwards from the front of the loudspeaker. The green semicircles show the low pressure zones.

If you have two sound sources, their pressure differences (relative to the average pressure) add. So, if you have two high pressures arriving at your eardrum, it will be pushed farther into your head than if only one of them arrived at your ear. Similarly, if you get two low pressures arriving at your eardrum, it will be pulled further out of your head than if only one of them was present. HOWEVER, if you have a high pressure and a low pressure arriving at the same time in the same place (for example, at your eardrum) then they cancel each other and, if they have the same magnitude, your eardrum won’t move at all and you won’t hear anything. (This is how noise-cancelling headphones work. The sound from the headphones is in theory identical to the sound coming to your ears from outside the headphones, except that it’s opposite in polarity, so the sum of the two sounds is nothing.)

 

The bottom plot is the result of adding the signals shown in the top and middle plots, moment by moment in time. For example, the red stars show the values at one moment in time. One plus one (the top two plots) equals two (the bottom plot).
Fig 1. The bottom plot is the result of adding the signals shown in the top and middle plots, moment by moment in time. For example, the red stars show the values at one moment in time. One plus one (the top two plots) equals two (the bottom plot).

 

The bottom plot is the result of adding the signals shown in the top and middle plots, moment by moment in time. For example, the red stars show the values at one moment in time. One plus one (the top two plots) equals two (the bottom plot).
Fig 2. The bottom plot is the result of adding the signals shown in the top and middle plots, moment by moment in time. For example, the red stars show the values at one moment in time. One plus negative one (the top two plots) equals nothing (the bottom plot).

 

Keep all that in mind as you read on…

 

Diffraction

It should not come as a surprise that a sound wave will bounce off a hard surface like a flat concrete wall. The question is “why?” The answer to this question can be complicated – but the simple version is that the molecules in a concrete wall are harder to move than the molecules in air – so we have a change in acoustic impedance. This is essentially a measure of how easily the molecules in the substance are moved by a sound wave… sort of… (Let’s leave it at that, since we really don’t need this article to be a thorough discussion of acoustic impedance.)

The interesting thing is that an acoustic wave will be reflected off any change in impedance. So, you don’t have to be going from a low impedance to a high impedance (as in the case of a sound wave trying to move from air into concrete). It will also reflect on a boundary where you change from a high to a low impedance (for example, a sound wave in concrete trying to get out into air – in this case, the sound wave will bounce off the surface of the concrete and move back into it rather than “leak” out into the surrounding air.).

Imagine yourself standing in a long tunnel. You clap your hands, and the sound wave travels down the length of the tunnel until it reaches the end – what happens then? Well, the answer is “two things”. Some of the sound leaks out of the tunnel. However, since the air inside the tunnel has a higher acoustic impedance than the air outside the tunnel (because the sound is freer to go where it wants on the outside), the end of the tunnel is a boundary where there is a change in acoustic impedance. And, as we saw in the last paragraph, this means that we will get a reflection. So, even though the end of the tunnel is open, it reflects your hand clap back into the tunnel. So, some sound leaks out and some reflects. (One way to really experience this is to notice your ears pop when you enter a long tunnel on a fast-moving train. When you first enter the tunnel, your ears pop because of the sudden change in pressure. Some time later, you might notice that your ears pop again. This is because the high-pressure wave front that the train made when it entered the tunnel travelled to the opposite end of the tunnel, bounced back and hit you again.)

If you didn’t know that the second sound was a reflection off the end of the tunnel (for example, you didn’t hear the first hand clap because you were wearing earplugs) you might think that it was a direct sound from someone down at the far end of the tunnel. So, if you’re not the person doing the clapping, but you’re in the tunnel with that person, you get two sounds – the direct sound and the reflection.

There is another, less obvious case where you have a change in acoustic impedance. This is when you have a sound wave travelling along next to the surface of something, and the surface ends. For example, if, in the animation at the top of this page, the surface of the loudspeaker cabinet was not as wide, there would be a corner where the face of the loudspeaker meets its side. At that corner, the acoustic wave front “sees” a change in acoustic impedance. Consequently, there is something like a reflection that starts at the corner. in essence, the corner of the loudspeaker is a boundary that radiates like a second sound source (just like the end of the tunnel in the example above).

So, if we modify the animation at the top of the page to include a narrower cabinet, the result would be something like the animation below.

 

As you can see there, the corner of the loudspeaker becomes a second source that radiates its own sound waves after the original, direct sound hits it.

This effect is called acoustic diffraction and it has some significant implications on the sound of a loudspeaker. This is directly because of the interference (see above…) between the direct sound from the loudspeaker driver and the secondary sound source caused by the corner.

Remember we saw above in Fig.1 that, when you have two high pressure zones that meet each other, you get more pressure than either one of them alone. Now take a look at the animation above and look for the places where the black curves from the two “sources” intersect. This is where you’ll get an increase in pressure, and therefore more energy than just the direct sound by itself. As you can see in Fig. 3, below, this means that you have an angle off-axis to the front of the loudspeaker where the signal is louder than it is directly on-axis. Of course, this also means that there will be some angles where you hear less (because the secondary wavefront from the corner cancels the direct sound) – these are where the red and green curves (the high and low pressure zones) intersect.

 

The straight lines show the places where the high pressure zones overlap each other (and the low pressure zones overlap each other), creating constructive interference and therefore higher sound pressure level.
Fig 3a. The straight lines show the places where the high pressure zones overlap each other (the red lines cross the red lines) and the low pressure zones overlap each other (the green lines cross the green lines), creating constructive interference and therefore higher sound pressure level (in other words, it’s louder).

 

As you can see in Fig 3a, there are different angles where the high pressures add to give you an even higher pressure (notice that the low pressures also add to give you an even lower pressure. The result is that, along those lines, you get constructive interference and therefore the sound is louder than it is elsewhere. I’ve only shown three such angles in this diagram – there are more. You might note as well that the origin of the high pressure lobes is not the centre of the loudspeaker driver (the piston shown in red). It’s somewhere between the primary and secondary sources (in this case, the loudspeaker driver and the corner).

 

The straight lines show the places where the high pressure zones overlap with the low pressure zones, creating destructive interference and therefore lower sound pressure level (in other words, it's quieter).
Fig 3b. The straight lines show the places where the high pressure zones overlap with the low pressure zones (the red lines cross the green lines), creating destructive interference and therefore lower sound pressure level (in other words, it’s quieter).

 

Fig 3b shows two angles where the high and the low pressures overlap, causing destructive interference and therefore cancellation. Therefore, the sound is quieter along those lines than it is elsewhere.

 

The real world

What does all of this mean in the real world?

Well, as you’ve probably already guessed, the first conclusion is that building a loudspeaker that has sharp corners is probably a bad idea. For example, if you wanted to build a loudspeaker, and you just put a tweeter on the front and made sharp right angles where the sides meet the front, you will have a problem with diffraction off those corners. As you can see in Figure 3, you will get a boost in the signal at some angles off-axis to the front of the loudspeaker, and some cancellation at other angles. The amount by which the signal will be boosted, the angles where you’ll have the effects, and the frequencies where you’ll have the problems are all dependent on the specific dimensions of the device. For example, the further away the loudspeaker’s corner from the driver, the lower the frequency that will be affected.

Let’s take a real-world example. The very first version prototype of the BeoLab 5 was really just a “normal” three-way loudspeaker that was used to test the ABC algorithm, So, there was a woofer in a cabinet with a microphone for the ABC development, but on top was just a small cabinet with a midrange driver and a tweeter, as you can see in Figures 4 and 5.

BeoLab 5 and its early prototype. This version was a late prototype of the lens geometry and the ABC demonstration / test device.
Fig 4. BeoLab 5 and its early prototype. This version was a late prototype of the lens geometry and the ABC demonstration / test device.

 

The original "conventional" tweeter and midrange used for comparison to the lens.
Fig 5. The original “conventional” tweeter and midrange used for comparison to the lens.

 

The original "conventional" tweeter enclosure used for comparison to the lens.
Fig 6. The original “conventional” tweeter enclosure used for comparison to the lens.

 

Figure 6 shows the “conventional” tweeter cabinet version of one of the BeoLab 5 prototypes which was placed on top of the white woofer cabinet shown in Figure 4 when the Acoustic Lens assembly was removed. As you can see, this is an example of how-not-to-make-a-loudspeaker (if you’re worried about diffraction). We have a tweeter in a flat surface and (some sharp-ish corners at the sides of the loudspeaker face). The result of this is that we have exactly the same problem shown in Figure 3a and 3b, above. We can see this in the measurement of the horizontal directivity of the loudspeaker, shown in Figure 7, below.

A directivity plot of the tweeter in a conventional cabinet shown in Figure 5. The X-axis is the frequency in Hz (ranging from 1.8 kHz to 20 kHz). The Y-axis is the horizontal angle of radiation where 0° is directly on-axis for the tweeter. The contour lines are in 0.5 dB increments and have been normalised to the on-axis response.
Fig 7. A directivity plot of the tweeter in the conventional cabinet shown in Figure 6. The X-axis is the frequency in Hz (ranging from 1.8 kHz to 20 kHz). The Y-axis is the horizontal angle of radiation where 0° is directly on-axis for the tweeter. The contour lines are in 0.5 dB increments and have been normalised to the on-axis response. The red ovals are peaks in the response caused by diffraction off the cabinet edges

It may be a little difficult to read this plot, so I’ll explain a little. The entire plot has been normalised to the on-axis magnitude response of the tweeter. In other words, the measurement doesn’t show the response of the tweeter – it shows how the response changes as you move around the loudspeaker in the horizontal plane.  The X-axis is the frequency of the signal in Hz, ranging from 1.8 kHz to 20 kHz. The Y-axis is the horizontal angle of radiation of the loudspeaker where 0° is directly on-axis, in front the tweeter. The lines in the plot can be thought of as a kind of topographical map with a difference of 0.5 dB per contour. So, if you think of a straight “ridge” in the plot along the 0° line in the middle, the plot generally falls off (in other words, the signal is quieter) as you move around to the side and back of the loudspeaker. You can see that, at the high frequencies, the lines are closer together which means that you lose more level at high frequencies than at low frequencies as you come around to the side of the loudspeaker. This is traditionally called loudspeaker “beaming”. The interesting thing to look at are the four red oval areas. The larger ones are centred around 3.2 kHz and ±40°. The smaller ones are up at about 7.5 kHz and  about ±15°. Because they’re in red, this means that they are louder than the on-axis response, so they are peaks in the topographical map. These peaks are the direct result of diffraction off the edge of the loudspeaker cabinet.  I count 4 red contour lines at the lower frequency peak, which means that we have a beam that is about 2 dB (remember, 0.5 dB per line * 4 lines) louder around 3 kHz at 40° off-axis to the loudspeaker.

This cabinet was built compare the directivity of a normal box-shaped loudspeaker to one with an Acoustic Lens. A close-up of the lens used for this comparison is shown below in Figure 8.

A first-generation Acoustic Lens on an early BeoLab 5 prototype.
Fig 8. A first-generation Acoustic Lens on an early BeoLab 5 prototype.

 

You’ll note in Figure 8 that the Acoustic Lens is slightly different from the final version (hence the “first-generation” qualifier) . This version also suffered from diffraction artefacts caused by the sharp edges where the face of the lens structure meets its side. This was corrected in the second generation version shown below in Figure 9.

A second-generation Acoustic Lens on an early BeoLab 5 prototype.
Fig 9. A second-generation Acoustic Lens on an early BeoLab 5 prototype.

 

Notice that the second-generation lens has curved transitions from face to side to reduce the diffraction problem. This curvature was eventually extended to wrap around the entire structure as can be seen in the photo of the final BeoLab 5 tweeter lens in Figure 10, below.

 

An Acoustic Lens on an BeoLab 5 tweeter.
Fig 10. An Acoustic Lens on an BeoLab 5 tweeter. Notice that the entire structure is curved from the face through the transition to the sides and to the back.

 

 

You may notice that the difference in these two designs was that the original one had sharp corners on the sides. The diffraction effects of these corners were easily visible in the first directivity measurements of the Lens, so the second prototype with the curved transition from front to side was made to eliminate this problem. The directivity measurement of the prototype shown in Figure 9 is seen below in Figure 11.

A directivity plot of the tweeter in a second-generation Acoustic Lens prototype shown in Figure 6. The X-axis is the frequency in Hz (ranging from 1.8 kHz to 20 kHz). The Y-axis is the horizontal angle of radiation where 0° is directly on-axis for the tweeter. The contour lines are in 0.5 dB increments and have been normalised to the on-axis response.
Fig 11. A directivity plot of the tweeter in a second-generation Acoustic Lens prototype shown in Figure 6. The X-axis is the frequency in Hz (ranging from 1.8 kHz to 20 kHz). The Y-axis is the horizontal angle of radiation where 0° is directly on-axis for the tweeter. The contour lines are in 0.5 dB increments and have been normalised to the on-axis response.

You’ll see in Figure 11 that there are two significant differences between the directivity of a tweeter in the prototype Acoustic Lens and a conventional cabinet (shown in Figure 7). The first difference is that the beaming effect (seen as a convergence of the contour lines at the high frequencies in Figure 7) does not happen with the lens. The contour lines are much more parallel resulting in a behaviour known as “constant directivity”. This is a way of saying that the loudspeaker has a directivity that is the roughly the same throughout its entire frequency range (rather than beaming in the high end).

The second difference is that the peaks in the 3 kHz and 8 kHz areas, seen in Figure 7, are gone. This is because there are no corners at the edge of the loudspeaker cabinet to cause diffraction. You may note a peak in the magnitude responses off-axis above 15 kHz. We actually don’t know what causes this, however, since it is so high in frequency and only +1 to +1.5 dB, and since this is still only a prototype, it wasn’t really considered to be a significant issue.

 

Wrapping up 

So, I’ve killed two birds with one stone in this article (or “two flies with one smack” as they say in Denmark). On the one hand,  we’ve seen that, if you’re worried about the directivity and/or the off-axis response of your loudspeaker (I know, the latter is a sub-set of the former…) sticking a tweeter (or a midrange, or a woofer, depending on dimensions and frequency ranges) on the front of a rectangular box is probably a really bad idea. (On the other hand, it’s a pretty easy, and therefore cheap, way to build a speaker, which is why such a design is so popular I guess…) And, on the other hand, we’ve seen one of the characteristics of Acoustic Lenses – being a more constant directivity than a tweeter-on-a-box. The fact that the tweeter mounted in an Acoustic Lens had less diffraction is not because of the Lens geometry in particular, but because of the shaping of its surroundings as part of the development process of BeoLab 5.

There are more stories like this one. For example, if you look carefully at the “plates” of the BeoLab 5 and the prototype in Figure 4 (the part the tweeter and midrange drivers are mounted in), you might notice that the prototype plates are flat, whereas the BeoLab 5 plates curve downwards. This is not because someone thought the curve would look pretty. This was because the circular edge of the prototype plates also caused diffraction, resulting in a higher-level lobe in the vertical plane. Sloping the plates downwards puts their sharp edges in the “shadow” of the plates themselves, reducing the diffraction effects. So, you can see that diffraction and its effects on directivity is one of the other issues that we worry about when we’re building a loudspeaker.

B&O Tech: But what if my room is Scandinavian?

#13 in a series of articles about the technology behind Bang & Olufsen loudspeakers

 

The following question recently arrived in my inbox via our customer service department.

“I am an admirer of B&O Hifi products as of over 20 years, but a great mystery for me is how you achieve great sound reproduction in the typically minimalist Scandinavian interior design environmment with polished floors, bare walls and bare glass windows. Effectively such environments are acoustical disasters !?!”

I thought that this was a great question – so it’s the topic of this week’s article.
Of course, you are correct. A room comprised of large flat reflective surfaces with little acoustical absorption has a very different acoustical behaviour from a recording or mastering studio where the final decisions about various aspects of a recording are made. And, consequently, this must have an effect on a listener’s perception of a recording played through a pair (assuming stereo reproduction) of loudspeakers in that room. The initial question to be asked is “what, exactly, are the expected effects of the room’s acoustical behaviour in such a case?” The second is “if the room has too much of an effect, how can I improve the situation (i.e. by adding absorption or changing the physical configuration of the system in the room)?” The third, and possibly final question is “how can we, as a loudspeaker manufacturer compensate (or at least account) for these effects?”
The effect a room’s acoustical behaviour has on a loudspeaker’s sound can, at a simple level, be considered under three general headings:
  1. early reflections
  2. room modes
  3. reverberation

Early Reflections

Early reflections, from sidewalls and the floor and ceiling, have an influence on both the timbre (tone colour) and the spatial characteristics of a stereo reproduction system. Let’s only think about the timbral effects for this article.
Fig 1. The sound arriving at a listener from a loudspeaker in a room with only one wall. Note that the sound arrives from two directions - the first is directly from the loudspeaker. The second is a "first reflection" off the wall.
Fig 1. The sound arriving at a listener from a loudspeaker in a room with only one wall. Note that the sound arrives from two directions – the first is directly from the loudspeaker. The second is a “first reflection” off the wall.
Let’s start by assuming that you have a loudspeaker that has a magnitude response that is perfectly flat – at least from 20 Hz to 20 kHz. We will also assume that it has that response regardless of which direction you measure it in – in other words, it’s a perfectly omnidirectional loudspeaker. The question is, “what effect does the wall reflection have on the measured response of the loudspeaker?”
Very generally speaking, the answer is that you will get a higher level at some frequencies (because the direct sound and the reflection add constructively and reinforce each other) and you will get a lower level at other frequencies (because the direct sound and the reflection work against each other and “cancel each other out”). What is potentially interesting is that the frequencies that add and the frequencies that cancel alternate as you go up the frequency range. So the total result looks like a comb (as in a comb that you use to comb your hair, if, unlike me, you have hair to comb). For example, take a look at Figure 2.
Fig 2. Distance to loudspeaker = 2 m. Distance to wall = 1 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
Fig 2. Distance to loudspeaker = 2 m. Distance to wall = 1 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
So, you can see in Figure 2 that, at the very low end, the reflection boosts the level of the loudspeaker by a little less than 6 dB (that’s two times the level!) at the listening position. However, as you go up in frequency, the total level drops to about 15 dB less before it starts rising again. As you go up in frequency, the level goes up and down. This alternation actually happens at a regular frequency spacing (i.e. a notch at every 200 Hz) but it doesn’t look regular because the X-axis of my plot is logarithmic (which better represents how we hear differences in frequency).
What happens if we move the wall further away? Well, two things will happen. The first is that the reflection will be quieter, so the peaks and notches won’t be as pronounced. The second is that the spacing of the peaks and notches in frequency will get closer together. For example, take a look at Figure 3.
Fig 3. Distance to loudspeaker = 2 m. Distance to wall = 3 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
Fig 3. Distance to loudspeaker = 2 m. Distance to wall = 3 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
Similarly, if we move the wall closer, we do the opposite, as in Figure 4.
Fig 2. Distance to loudspeaker = 2 m. Distance to wall = 0.25 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
Fig 4. Distance to loudspeaker = 2 m. Distance to wall = 0.25 m. Wall is perfectly reflective and the loudspeaker is perfectly omnidirectional.
So, if you have a room with only one wall which is perfectly reflective, and you have a perfectly omnidirectional loudspeaker, then you can see that your best option is to either put the loudspeaker (and yourself) very far or very close to the wall. That way the artefacts caused by the reflection are either too quiet to do any damage, or have an effect that starts at too high a frequency for you to care. Then again, most room have more than one wall, the walls are not perfectly reflective, and the loudspeaker is not perfectly omnidirectional.
So, what happens in the case where the loudspeaker is more directional or you have some fuzzy stuff on your walls? Well, either of these cases will have basically the same effect in most cases since loudspeakers are typically more directional at high frequencies – so you get less high end directed towards the wall. Alternatively, fuzzy stuff tends to soak up high frequencies. So, in either of these two cases, you’ll get less high end in the reflection. Let’s simulate this by putting a low pass filter on the reflection, as shown in Figure 5, 6 and 7 which have identical distances as the simulations in Figures 2, 3, and 4 – for comparison.
Fig 5. Distance to loudspeaker = 2 m. Distance to wall = 1 m. Wall is absorptive at high frequencies and/or the loudspeaker is directional.
Fig 5. Distance to loudspeaker = 2 m. Distance to wall = 1 m. Wall is absorptive and/or the loudspeaker is directional at high frequencies .
Fig 2. Distance to loudspeaker = 2 m. Distance to wall = 3 m. Wall is absorptive at high frequencies and/or the loudspeaker is directional.
Fig 6. Distance to loudspeaker = 2 m. Distance to wall = 3 m. Wall is absorptive and/or the loudspeakers is directional at high frequencies.
Fig 2. Distance to loudspeaker = 2 m. Distance to wall = 0.25 m. Wall is absorptive at high frequencies and/or the loudspeaker is directional.
Fig 7. Distance to loudspeaker = 2 m. Distance to wall = 0.25 m. Wall is absorptive and/or the loudspeaker is directional at high frequencies.
What you can see in all three of the previous plots is that, as the high frequency content of the reflection disappears, there is less and less effect on the total. The bottom plot is basically a proof of the age-old rule of thumb that says that, if you put a loudspeaker next to a wall, you’ll get more bass than if it’s farther from the wall. Since there is not much high frequency energy radiated from the rear of most loudspeakers, Figure 7 is a pretty good general representation of what happens when a loudspeaker is placed close to a wall. Of course, the exact behaviour of the directivity of the loudspeaker will be different – but the general shape of the total curve will be pretty similar to what you see there.
So, the end conclusion of all of this is that, in order to reduce undesirable artefacts caused by a wall reflection, you can do any combination of the following:
  • move the loudspeaker very close to the wall
  • move the loudspeaker farther front the wall
  • sit very close to the wall
  • sit farther away from the wall
  • put absorption on the wall

However, there is one interesting effect that sits on top of all of this – that is the fact that what you’ll see in a measurement with a microphone is not necessarily representative of what you’ll hear. This is because a microphone does not have two ears. Also, the direction the reflection comes from will change how you perceive it. A sidewall reflection sounds different from a floor reflection. This is because you have two ears – one on each side of your head. Your brain uses the sidewall reflections (or, more precisely, how they relate to the direct sound) to determine, in part, how far away a sound source is. Also, since, in the case of sidewall reflections, your two ears get two different delay times on the reflection (usually), you get two different comb-filter patterns, where the peaks in one ear can be used to fill in the notches in the other ear and vice versa. When the reflection comes from the floor or ceiling, your two ears get the same artefacts (since your two ears are the same distance to the floor, probably). Consequently, it’s easily noticeable (and it’s been proven using science!) that a floor or ceiling reflection has a bigger timbral effect on a loudspeaker than a lateral (or sideways) reflection.

Room modes

 Room modes are a completely different beast – although they exist because of reflections. If you pluck a guitar string, you make a deflection in the string that moves outwards until it hits the ends of the string. It then bounces back down the string, bounces again, etc. etc. See the diagrams and animations on this page – they might help. As the wave bounces back and forth, it settles in to a total result where it looks like the string is just bouncing up and down like a skipping rope. The longer the string, the lower the note, because it takes longer for the wave to bounce back and forth on the string. You can also lower the note by lowering the tension of the string, since this will slow down the speed of the wave moving back and forth on it. The last way to lower the note is to make the string heavier (i.e. by making it thicker) – since a heavier string is harder to move, the wave moves slower on it.
The air in a pipe behaves exactly the same way. If you “pluck” the air in the middle of a pipe (say, by clapping our hands, or coughing, or making any noise at all) then the sound wave travels along the pipe until it hits the end. Whether the end of the pipe is capped or not, the wave will bounce back and travel back through the pipe in the opposite direction from whence it came. (Whether the pipe is closed (capped) or open only determines the characteristic of the reflection – there will be a reflection either way.) It might help to look at the animations linked on this page to get an idea of how the air molecules behave in a pipe. As the wave bounces back and forth off he two ends of the pipe, it also settles down (just like the guitar string) into something called a “standing wave”. This is the pipe’s equivalent of the skipping rope behaviour in the guitar string. The result is that the pipe will resonate or ring at a note. The longer the pipe, the lower the note because the speed of the sound wave moving in air in the pipe stays the same, but the longer the pipe, the longer it takes for the wave to bounce back and forth. This is basically how all woodwind instruments work.
What’s interesting is that, when it comes to resonating, a room is basically a pipe. If you “pluck” the air in the room (say, by putting sound out of a loudspeaker) the sound wave will move down the room, bounce off the wall, go back through the room, bounce of the opposite wall, etc. etc. etc. (other things are happening, but we’ll ignore those). This effect is most obvious on a graph by putting some sound in a room and stopping suddenly. Instead of actually stopping, you can see the room “ringing” at a frequency that gradually decays as time goes by. However, it’s important to remember that this ringing is always happening – even while the sound is playing. So, for example, a kick drum “thump” comes out of the speaker which “plucks” the room mode and it rings, while the music continues on. You can see this in Figure 8, below.
Fig 8. The concept of the effect of a room mode. The sound coming out of the loudspeaker is shown on the top plot, in black. The response in the room is shown in blue. You can see there that the room keeps "ringing" at a frequency after the sound from the loudspeaker stops. The red plot on the bottom is the difference between the two plots - in other words, the "sound" of the room mode in isolation.
Fig 8. The concept of the effect of a room mode. See the text below for an explanation.
Figure 8 shows the concept of the effect of a room mode. The sound coming out of the loudspeaker is shown on the top plot, in black. The response in the room is shown in the middle plot in blue. You can see there that the room keeps “ringing” at a frequency after the sound from the loudspeaker stops. The red plot on the bottom is the difference between the two plots – in other words, the “sound” of the room mode in isolation (note that it’s at a different scale than the top two plots to make things easier to see).

There are two audible effects of this. The first is that, if your music contains the frequency that the room wants to resonate at, then that note will sound louder. When you hear people talk of “uneven bass” or a “one-note-bass” effect, one of the first suspects to blame is a room mode.

The second is that, since the mode is ringing along with the music, the overall effect will be muddiness. This is particularly true when one bass note causes the room mode to start ringing, and it keeps ringing when the next bass note is playing.  For example, if your room rings on a C#, and the bass plays a C# followed by a D – then the room will be ringing at C#, conflicting with the D and resulting in mud. This is also true if the kick drum triggers the room mode, so you have a kick drum “plucking” the room ringing on a C# all through the track. If the tune is in the key of F, then this will not be pretty.

 

If you would like to calculate a prediction of where you’ll have a problem with a room mode, you can just do the following math:

metric version: room mode frequency in Hz = 172 / (room length in metres)

imperial version: room mode frequency in Hz = 558 / (room length in feet)

Your worst modes will be the frequencies calculated using either of the equations above, and multiples of them (i.e. 2 times the result, 3 times the result, and so on).

So, for example, if your room is 5 m wide, your worst-case modes will be at 172 / 5 = 34.4 Hz, as well as 68.8 Hz, 103.2 Hz and so on. Remember that these are just predictions – but they’ll come pretty close. You should also remember that this assumes that you have completely immovable walls and no absorption – if this is not true, then the mode might not be a problem at all. (If you would like to do a more thorough modal analysis of your listening room, check out this page as a good start.)

Sadly, there is not much you can do about room modes. There are ways to manage them, including, but not exclusive to the following strategies:

  • make sure that the three dimensions of your listening room are not related to each other with simple ratios
  • put up membrane absorbers or slot absorbers that are tuned to the modal frequencies
  • place your loudspeaker in a node – a location in a room where it does not couple to a problematic mode (however, note that one mode’s node is another mode’s antinode)
  • sit in a node – a location in a room where you do not couple to a problematic mode (see warning above…)
  • use room correction DSP software such as ABC in the BeoLab 5

 

Reverberation

Reverberation is what you hear when you clap your hands in a big cathedral. It’s the  collection of a lot of reflections bouncing from everywhere as you go through time. When you first clap your hands, you get a couple of reflections that come in separated enough in time that they get their own label – “early reflections”. After that, there are so many reflections coming from so many directions, and so densely packed together in time, that we can’t separate them, so we just call them “reverberation” or “reverb” (although you’ll often hear people call it “echo” which is the wrong word to use for this.

Reverb is what you get when you have a lot of reflective surfaces in your room – but since it’s so irregular in time and space, it just makes a wash of sound rather than a weird comb-filter effect like we saw with a single reflection. So, although it makes things “cloudy” – it’s more like having a fog on your glasses instead of a scratch. Think of it like the soft focus effect that was applied to all attractive alien women on the original Star Trek – you lose the details, but it’s not necessarily a bad thing.

 

So what are you gonna do about it?

Fine, this is a short-form version of what a room’s acoustics does to the sound of a loudspeaker, but how do we, as a manufacturer of loudspeakers, ensure that our products can withstand the abuse that your listening room will apply to the sound? Well, there are a number of strategies that we use to do what we can…

1. ABC. The BeoLab 5 has a proprietary system built-in called Adaptive Bass Control or ABC. Pressing a button at the top of the loudspeaker starts a measurement procedure that is performed using a built-in microphone that measures the loudspeaker’s behaviour in two locations. Actually, what it’s doing is looking at the difference in the loudspeaker’s response in those two positions of the microphone to determine the radiation resistance that the loudspeaker “sees” as a result of reflective surfaces in the room. The ABC algorithm then creates a filter that is used to “undo” the effects of some of the low-frequency effects of the room’s acoustics. For example, if the radiation resistance indicates that the loudspeaker is close to a wall (which, as we saw above, will boost the bass) then the filter will reduce the bass symmetrically. That way, the loss in the filter and the gain due to the wall will cancel each other.

2. Position switches. ABC in the BeoLab 5 is a very customised filter that, in part, will adjust the loudspeaker’s response for placement near a wall or in a corner. Almost all of the other BeoLab loudspeakers (and other sound systems such as the BeoPlay A8 and A9, for example), include a manual-adjusted “position switch”. This allows you to use one of three filters that we have customised in the development of the loudspeaker to account for its behaviour according to whether you have placed it away from a reflective surface (“Free”), near one surface (“Wall”) or in a Corner. This is not just a filter that adjusts the bass level. The three filters for “free”, “wall”, and “corner” have been calculated using three dimensional measurements of the acoustical behaviour of the loudspeaker. So, the filters for the BeoLab 3 are completely different from those for the A9, for example, because they have very different directivity characteristics.

3. Sound design in multiple rooms. As I talked about in a previous posting, when we do the sound design of all of our loudspeakers, we tune each of them in at least 4 or 5 rooms with very different acoustical behaviours ranging from a very “dead” living room with lots of absorptive and diffusive surfaces to a larger and very “live” space with a minimalistic decorating, and large flat surfaces (just like the description in the original question). Once we have a single sound design that is based on the common elements those rooms, we test the loudspeakers in more rooms to ensure that they’ll behave well under all conditions.

 

Wrap-up

Of course, I haven’t covered everything there is to know about room acoustics here. And, of course, you can’t expect a loudspeaker to sound exactly the same in every room. If that were true, there would be no such thing as a “good”concert hall. A room’s acoustical behaviour affects the sound of all sound sources in the room. On the other hand, humans also have an amazing ability to adapt – in other words you “get used to” the characteristics of your listening room. Back when I was working as a part-time recording engineer in Montreal, I did a lot of recordings in churches. Typically, we (the producer and I) would set up a control room with loudspeakers in a back room, and the musicians would sit out in the church. When we arrived to set up the gear, the first thing was to set up the monitor loudspeakers and a CD player, and we would play CD’s that we knew well while we set up everything else. That way, we would “learn” the characteristics of the control room (since we already knew what was on the discs and the characteristics of the monitor loudspeakers). So, if all of our CD’s sounded like that had too much bass, then we should do a recording with too much bass – it was the fault of the control room.

However,  there is no debate that, due to lots of issues (the first two that come to mind are frequency range and directivity) two different loudspeakers will behave differently from each other in two different rooms. In other words, if you listen to loudspeaker “A” and loudspeaker “B” in a showroom of a shop, you might prefer loudspeaker “A” – but if you took them home, you might prefer loudspeaker “B”. This would not be surprising, since what you hear is not only the loudspeaker but the loudspeaker “filtered” by the listening room. This is exactly why, when you are buying a loudspeaker, you should audition it in your home in order to ensure that you will be happy with your purchase. And THIS is why you can arrange a home demonstration of Bang & Olufsen loudspeakers through your dealer.