{"id":1211,"date":"2013-12-13T08:03:01","date_gmt":"2013-12-13T06:03:01","guid":{"rendered":"http:\/\/www.tonmeister.ca\/wordpress\/?p=1211"},"modified":"2018-12-14T09:44:16","modified_gmt":"2018-12-14T07:44:16","slug":"bo-tech-what-are-subwoofers-really-for","status":"publish","type":"post","link":"http:\/\/www.tonmeister.ca\/wordpress\/2013\/12\/13\/bo-tech-what-are-subwoofers-really-for\/","title":{"rendered":"B&O Tech: What are subwoofers REALLY for?"},"content":{"rendered":"

#6 in\u00a0a series of articles<\/a>\u00a0about the technology behind\u00a0Bang & Olufsen<\/a>\u00a0loudspeakers<\/strong><\/p>\n

 <\/p>\n

The Setup<\/h2>\n

Back in a previous posting<\/a>, I said something that could be perceived as interesting… The short version of what I said there was that, if you’re making a DSP-based active loudspeaker (like all of the new loudspeakers in the B&O portfolio), you can essentially make it sound like whatever you want. You do this by adding filters in the digital signal processing (DSP). (Let’s assume\u00a0for this article that\u00a0we’re only talking about the on-axis magnitude response of the loudspeaker, and we’re working in an anechoic environment (aka a “free field” situation), since that will keep things simple.) This means that, if I can apply enough boosts and cuts, I can get any magnitude response I want out of the loudspeaker. In other words, I can have a 1″ tweeter that plays with a perfectly flat response from 20 Hz to 20 kHz.<\/p>\n

However, there are some serious restrictions on this statement. As a minor example, if there is a problem with diffraction the only way to change that is to modify the shape of the loudspeaker cabinet (if you don’t know what diffraction is, don’t worry – it will not be mentioned again in this article).<\/p>\n

However, there is one GIANT restriction on the statement that we’ll look at this week. This is a question of how loudly you want to play. So let’s look at that.<\/p>\n

In order to make sound, a loudspeaker driver has to move in and out – this pushes and pulls the air molecules in front of it, creating small areas of higher pressure and lower pressure (relative to today’s natural barometric pressure) that radiate outwards, away from the driver. Those variations in pressure push and pull your eardrum in and out of your head which, in turn cause stuff to happen in your inner ear which, in turn causes stuff to happen in your brain – but that is all outside the scope of this discussion.<\/p>\n

Back to the loudspeaker – it has to move in and out. The louder you want to play (more accurately, the higher the Sound Pressure Level (SPL), the more it has to move in and out. Also, the lower in frequency you want to play,\u00a0he more it has to move in and out (to keep the same SPL).<\/p>\n

\"The<\/a>
The red arrow shows the direction of movement of the loudspeaker driver required to make a positive (or high) pressure. The driver has to go the other way (into the cabinet) to make a negative (low) pressure.<\/figcaption><\/figure>\n

 <\/p>\n

The real problem is the second of these, since the rule of thumb is that, every time you go down one octave (in other words, you divide the frequency by 2) you need to quadruple the excursion of the driver (the amount it moves in and out).<\/p>\n

Let’s look at an example. The figure below illustrates the excursion required for different sizes of loudspeaker drivers in order to create a sound pressure level of 60 dB SPL (which is not very loud – but is a typical sort of listening level) at 1 m (which is a good approximation for how loud it will be all over your living room due to something called the room’s “critical distance” – we’ll talk about that in the future).<\/p>\n

Notice that, for the 15″ woofer, it only has to move 0.08 mm out of the box (and 0.08 mm into the box) to produce a 20 Hz signal at 60 dB SPL. This is not very much movement. By comparison, the 4″ woofer has to move 1.2 mm which is much more than 0.08 mm, but still not much.<\/p>\n

To bring this into the real world, this means that a woofer taken out of a BeoLab 3<\/a> (which is 4″ in diameter) would have to move 14 times farther than a woofer from a BeoLab 5<\/a> (15″ woofer) to produce the same output. This is because the 4″ woofer is smaller than the 15″, so to move the same number of air molecules, we have to move it more. (actually, what we’re really thinking about here is how many litres of air we’re moving, but that might be too much detail…)<\/p>\n

 <\/p>\n

\"The<\/a>
The excursion of a driver (of different diameters) required to generate a signal of 60 dB SPL at 1 m from the front of the driver. Note that this assumes that your driver is mounted in a hole in the wall, not a real loudspeaker box (see text for the implications of this).<\/figcaption><\/figure>\n

 <\/p>\n

Let’s consider the practical implications of this graph. Since a BeoLab 3 woofer can<\/em> move 1.2 mm in and out (and, of course, a BeoLab 5 woofer can move 0.08 mm). Both loudspeakers are able to produce a 20 Hz tone at 60 dB SPL. Therefore, if we choose to do so, we can make both loudspeakers have a magnitude response that was flat from 20 Hz to 20 kHz\u00a0at this listening level<\/em> (or quieter).<\/em><\/p>\n

Let’s turn up the volume knob. We’ll go up to 80 dB SPL which is a bit loud, but certainly not enough to get the party going… Now we need to move the 15″ woofer 0.8 mm (still not very much…) and the 4″ woofer 11.6 mm to produce 20 Hz at 80 dB SPL. Of course, the BeoLab 5 woofer can easily move 0.8 mm, but 11.6 mm is too far to go for the BeoLab 3 woofer. So, if we didn’t have ABL<\/a>\u00a0to protect things from moving too far<\/em>, we would not be able to tune the BeoLab 3 to be flat down to 20 Hz – we would have to “roll off” the low frequencies so that 20 Hz was not as loud as the frequencies above 20 Hz in order to prevent it from causing the woofer to move to far when you turn up the volume. (For example, we could tune it to be flat down to 40 Hz instead of all the way to 20 Hz.)<\/p>\n

 <\/p>\n

\"80dBspl\"<\/a>
The excursion of a driver (of different diameters) required to generate a signal of 80 dB SPL at 1 m from the front of the driver. Note that this assumes that your driver is mounted in a hole in the wall, not a real loudspeaker box (see text for the implications of this).<\/figcaption><\/figure>\n

 <\/p>\n

Let’s go further, just to make things really obvious. We’ll turn up the volume to 110 dB SPL (which is very loud). Now, to get a 20 Hz tone out at this level, the 15″ driver will have to move 2.6 cm and the BeoLab 3 woofer would have to move 36.6 cm (which is silly). So, here it is obvious that, if we want to build the BeoLab 3 to play 110 dB SPL, we will have to use ABL or limit its low frequency content (or use some balance of those two things – a little ABL and a little higher low-frequency limit).<\/p>\n

 <\/p>\n

\"110dBspl\"<\/a>
The excursion of a driver (of different diameters) required to generate a signal of 110 dB SPL at 1 m from the front of the driver. Note that this assumes that your driver is mounted in a hole in the wall, not a real loudspeaker box (see text for the implications of this).<\/figcaption><\/figure>\n

 <\/p>\n

Let’s look at this in another, more intuitive way. If we wanted a BeoLab 3 woofer to play as loudly as a BeoLab 5 woofer can play, at its peak excursion in and out of the cabinet, it would look like the figure below.<\/p>\n

 <\/p>\n

\"A<\/a>
A to-scale representation of how much the woofer on a BeoLab 3 would have to move to play as loudly as the woofer on a BeoLab 5.<\/figcaption><\/figure>\n

 <\/p>\n

The Implications<\/h2>\n

So, what does this mean? Well, it means two things:<\/p>\n