SPL, power and dBs

[MarkOne]

I know, I should know this.

A +3dB equates to a doubling of power, but a number of sources I’ve read are quoting +10dB increase required to get a perceived doubling in loudness

For instance here

So what is the actual figure you should be thinking about when trying to compare PA speakers?

[Wonks]

+6dB SPL is a doubling of the actual sound pressure level, which directly relates to volume/loudness in a physics sense. But the ear/brain and loudness thing is complex, so there's no straight relationship. For a start a 10dB drop in SPL is perceived as less of a change than a 10dB increase. So we know its not nice and linear.

It's going to be somewhere between 6dB and 10dB. but it can all depend on the starting volume, the frequency content and the person listening. Just think of Fletcher-Munson curves and you'll see that increases in treble and bass content will have a different effect depending on the starting loudness level. So the amount of bass or treble when playing back music may give a different perception of loudness compared to speech at the same SPL.

The frequency range of your hearing will also have an affect on the perceived loudness.

I always think that it's a hard subject to pin down, because often you have no real reference. It's not like you can see different sound levels like you can see two columns of bricks and say by how much more one is taller than the other. You can play two test tones at different levels on headphones one after the other, but even then 'double the volume' is still subjective.

Lets say there are two PAs set up in two different soundproof rooms off a common hallway. Going from PA room 1 and back into the silent hallway and then into PA room 2, you'll be able to say which room was louder, but I really doubt you'd truly be able to say with confidence that Room B was twice as loud as room A.

A bit louder, louder, a lot louder and f**ing loud are typical human frames of reference. But you rarely think, "that's 7/10 louder than before". So even 'double the volume' is going to be subjective and dependent on circumstances. With fresh ears, 'double' might be several more dB SPL than if you're tired at the end of the day.

And the same PA set up in two rooms of different sizes and shape will give a different SPL level once you get more than a few feet away, despite the PA being set to the same output, just to the way the sound is being reflected differently and the interactions between direct and reflected sound.

[Hugh Robjohns]

Wonks makes a lot of good points. This is a very slippery subject to tie down...

But just from the point of view of guide numbers, you are right that 3dB is a doubling/halving of acoustic power, 6dB is a doubling/halving of SPL, and 10dB is a doubling of perceived volume... to most people.

[muzines]

But just from the point of view of guide numbers, you are right that 3dB is a doubling/halving of acoustic power, 6dB is a doubling/halving of SPL, and 10dB is a doubling of perceived volume... to most people.

Audio is very unintuitive. I wish the universe just came with good documentation, rather than leaving this all to scientists and engineers and mathematicians to reverse-engineer and figure out. All this science is very time and resource-consuming, and a good manual would sort all that right out from the get-go.

I'd skip straight to the "dark matter" chapter - I mean, what the heck's going on with that?

Science - it's just the process of creating nature's manual.

Well, I guess we all know that good manuals are hard to make...

[ef37a]

Loudness, watts and its subjective effects certainly are a slippery subject and no more so I would aver than in the guitar amplifier/speaker scene.

12" speaker chassis from several different manufacturers might have a sensitivity rating of 100dB SPL for one watt at one mtr but listen to them all in turn and it is very plain some are 'louder' than others.

This is because some drive units have a fairly smooth response and others are 'shouty' in the mid band just where our (well, MOST people's!) hearing is most sensitive. The SPL meter takes no account of that.

Then, what's a watt? You might think that if you put 2.82V rms across an 8 Ohm voice coil you are pumping in a watt of pink noise. You are not because the coil is not 8R over the bandwidth of the signal.

Amplifiers are also hard to pin down. The ad might call it a 30W guitar amp but at what level of distortion? Then all valve amps and almost all transistor are powered from unregulated supplies. Your 30W could be well up or down on that figure depending on your mains voltage. Not that it matters much. 22W or 38, you won't notice the difference.

Dave.

[Wonks]

I would still question the 10dB loudness doubling figure. A lot of the research is from many years ago, and tough not recent, Richard M Warren's 1973 paper in the December issue of the American Journal Of Psychology* clearly shows a 6dB law (between 45dB SPL and 90dB SPL) in the perceived halving of volume between two white noise test tones, and so tying-in the linear relationship between SPL and perceived loudness.

Previous studies had much greater estimations of the change required (some up to 20dB) but the average was around 9dB.

But the previous method of testing, with a test subject being given numerous test samples in succession, was found to result in the estimation of the value of dB change required for half-volume to increase as the number of samples increased. This is apparently to be expected in this sort of repeated experiment and is called 'Centripetal Range Error' (I have no idea what this is ATM).

So instead, Warren tested 650 people with only one comparison sample each. They could switch back and forth between the two loudness levels by pressing a button, so were free to check as many times as they wanted. They then wrote down a score between 0 and 100, where 100 represented the louder sample and 0 was silence

Whilst there were obviously variations, the linear correlation between different degrees of attenuation and the difference in SPL was very strong. it was also very noticeable that a 4dB difference in SPL was clearly perceived as significantly greater than half loudness and 8dB as significantly less than half-loudness.

Very similar results (within a percent or so) were achieved using both headphones and speakers and again, 4dB and 8dB changes were definitely heard as less and more than half-volume.

The initial tests were done with a reference 85dB SPL, with 4dB, 6dB and 8dB drops in SPL.

More experiments were carried out with different white noise SPLs from 100dB SPL to 35dB SPL. using a 6dB drop in SPL as the reference drop. Again, each of the 180 subjects in this test were given only one comparison test.

The results varied slightly but a 6dB SPL drop was perceived as a bit quieter than half-volume (40 out of 100) at 35dB SPL, within a couple of percent of half-volume between and 45dB and 90dB SPL, and a bit more than half-volume (60 out of 10) at 100dB.

So you may well need more than 6dB once things get beyond 90dB SPL to change the perceived volume, but the volume level the audience hears shouldn't really get much louder than that, even if the speakers are putting out a lot more.

Some of the experiment was repeated, using the quieter sound as the base level of 100, with the subjects asked to give a numerical value to the relative loudness of the second signal. No maximum value limit was stated. The second signal had an SPL either 6dB or 10dB louder.

Interestingly, the mean and median response for both levels was 200, i.e. twice as loud!

We are very good at picking numbers we feel safe with, so there's always a tendency to pick 40, 50, 60 etc rather than 67 or 53. Likewise if given a value of 100 and asked to estimate the value of a louder sound, the tendency is to go for a nice multiple.

So the first lot of experiments were repeated (different dB drops), but this time with a line to record relative volume estimates, with one end silence and the other the loud sound. No numbers involved, just a mark on the line.

The results were less linear this time, with smaller drops perceived as bigger drops than previously, and the bigger drops perceived as not as big as previously, but still with the -6dB drop pretty much hitting the 50% mark (about 48%).

However there are provisos on the figures above, this is for white noise.

Pink noise would probably have been a better test sound for use with music, as the overall frequency levels (equal energy per octave) are similar. That may gave slightly different results.

Human speech also has a different perceived loudness halving factor. Non-reverberant speech was perceived strongly as being half-volume with a 12dB attenuation through headphones - the brain is very good at picking out speech so it seems louder than other sounds. 10dB and 14dB drops were seen as significantly louder and quieter respectively than the 12dB figure.

Once significant reverb is introduced, the ability to determine a halving of speech intensity becomes very confused, and 8 to 16db drops in SPL all registered as around the halving of volume mark. Once the sound was made pretty unintelligible through excessive reverb levels, the half-volume level went up to a 7dB drop in SPL, so not far off that for noise.

(As an aside, it turns out that humans are very good at raising the loudness of their voice to match the distance away someone is. Move someone twice as far away and the person speaking will naturally raise their voice by pretty much 6dB to compensate for the inverse-square law and keep the volume heard by the listener the same. I've seen this in several papers.)

So, based on this, I'd err in general towards a 6dB dB change in music SPL being a halving of volume, provided the overall SPL value at the ears is 90dB or less. We humans seem to be less clear about what constitutes a doubling of volume, even though it's exactly the same sound difference.

A lot of the time it's the way the questions are asked and the numbers used that can make a big difference, which is why it's more accurate to ask about a reduction in volume than an increase. Tell someone the quieter sound is 100 and give a scale of 100 to infinity, 100 to 600 or 100 to 300 for the louder noise and you'll probably get three different answers as the numbers involved impose limits which may or may not constrain our perception and how we answer.

Ask about a reduction in volume, and our brain has a much better frame of reference.

So it's probably more accurate to talk about one PA system sounding half as loud as another one rather than one sounding twice as loud.

I'd like to know if there are any similar papers using pink noise or music as the test source but with the same single sample per test subject method, and if their conclusions were significantly different.

*I found the paper here on JFOR. Sign up to it and you can view the papers on the website (up to 100 a month) for free, but it costs to download them.

https://www.jstor.org/stable/1422087?re ... b_contents

[RichardT]

Thanks for that Wonks. I think that white noise is a strange choice - outside audio circles nobody normally hears it.

[Wonks]

White noise covers all frequencies, and was easily created in early electronic circuits. If you are doing true equal volume tests, then you do need the frequencies present to be of equal amplitude - so white noise was used. I pity the poor test people who had to listen to it multiple times.

I'm not surprised those tests that had one tester listen to 30 samples in close succession, rather than 30 testers listen to one sample, started giving skewed results.