On this episode of Ask The Expert, Otto explains how to calculate loudness – perfect if you've ever tried to figure out in advance how loud your system is going to be in a given environment. Look no further – we've got tips aplenty that go beyond the often less-than-useful official product specifications!
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If I have a speaker that – according to the specification sheet – has a sensitivity of 86 decibels, and my amplifier has 100 watts of output, how loud would the sound actually be in my listening position, which is four meters away?
This is a very interesting question because there are a lot of calculators which you can find online, and are designed you figure out the level of loudness at a given distance from the speaker, whilst also taking the amplifier's power into account.
The problem is that a lot of these calculators are making some wrong assumptions, which can lead to bad results. We recommend that you follow our tips here for a more successful calculation.
So the first step of figuring out how loud the speaker actually is in the listening position is, we look at the sensitivity. (for a more in-depth look at speaker sensitivity, we recommend that you check out this episode.)
Let's say that the sensitivity is specified as 86 decibels at 2.83 volts. We'd like this second figure in watts, and for that we need to look at the impedance (i.e ohms). If our speaker has an impedance of 4 ohms, it would mean that our 2.83 volts is equivalent to 2 watts. (2.83² / 4 = 2.00) See fig 1.
We already know that the sensitivity is 86 dB, and now we know that's at 2 watts. From here we can measure the maximum capability of the amplifier. If the amplifier is 100 watts, we can figure out that that is 50 times our 2 watts. Using a specific calculation (see fig 2.) we can figure out that that amounts to 17 decibels which – when added to the 89 decibel sensitivity rating – results in 103 decibels.
fig 1.
fig 2.
From this might assume that our maximum SPL at one metre distance is 103 decibels. In fact when you place the speaker inside the listening room, you get some gain from the room itself – especially when placing it close to the wall. The specification sheet assumes that you have your speaker in an anechoic chamber, but you don't, you have it inside your listening room, where the walls are adding some output to the speaker – as much as four to five decibels – and particularly in the lower frequencies.
This added room gain is highly frequency dependent, so the actual addition to the total SPL depends on the frequency range of the speakers and the content of the music, and that's rather complicated to calculate. However, all in all, it's pretty reasonable to assume an additonal 4 to 5 dB on top of what we've determined from specification sheet, by which point we're getting up to around 108 dB (see fig 3.)
fig 3.
fig 4.
Finally, we also need to take the distance from that aforementioned one metre specification to your couch into account: let's say that that is four metres and we'll come back to that in a moment.
The online calculators we mentioned at the beginning of the article make an assumption of a 6 dB fall decrease in output per doubling of distance from the speaker, but this assumption is only true of anechoic environment and – in a normal living room – what you actually get is a decrease in output of around three to four dB per doubling of distance. Therefore, instead of two times 6 dB, you need to subtract only two times 3 to 4 dB when going from one metres to four metres – let's say therefore 8 dB (see fig 4.)
In reality then, the total output of the speaker in the listening position will probably be over 100 dB – a lot louder than the 90 dB that would have been concluded from one of these online calculators. As you can see, our method of calculation – by taking the actual listening environment into account – gives a much more accurate representation of the resultant loudness.
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