JohnMac Posted July 12, 2011 Share Posted July 12, 2011 Good Folks of the Blue Room, I'm currently looking at buying some loudspeakers and have become stuck on Sensitivity. I've forgotten if in these figures if the formula is 10log(Ratio), or 20log(Ratio). If a difference of 4dB is quoted, does this mean I get 2.5 times more volume for the same amplifier power? Amazing what one forgets with time. Link to comment Share on other sites More sharing options...
J Pearce Posted July 12, 2011 Share Posted July 12, 2011 Acoustic sound pressure (dB SPL) is based on a 20log ratio. 6dB is a mathematical doubling of output power, except our ears don't quite perceive it like that, especially at higher SPLs. There is also the disparity between measured and calculated figures, and at what frequencies and time durations the measurements were taken i.e. pink noise for 1min or 1kHz burst for 1ms... Sensitivity is one of the numbers worth looking at, but nothing beats your ears for deciding what speakers to buy! Link to comment Share on other sites More sharing options...
Brian Posted July 12, 2011 Share Posted July 12, 2011 It's generally reckoned, as a rule of thumb, that the ear perceives a 10dB difference as being twice as loud. Link to comment Share on other sites More sharing options...
Simon Lewis Posted July 12, 2011 Share Posted July 12, 2011 Sensitivity is the sound pressure level measured at 1m on axis with 1W (or 2.83V into 8 Ohm) applied. The problem (as Brian suggests) is that we perceive "volume" somewhat subjectively. As a rule of thumb we perceive an increase in sound pressure of 10dB to be a doubling of 'volume'. There is a useful relationship that gives the theoretical maximum output of a speaker: SPL = reference sensitivity + 10log applied power So a 1000W 96dB @ 1W @ 1m speaker should give 96+30 = 126dB. This doesn't take power compression into account. Acoustic pressure requires 20Log terms, intensity and power, 10Log terms. Acoustic sound pressure (dB SPL) is based on a 20log ratio. 6dB is a mathematical doubling of output power, I think you meant to say, 6dB is a doubling of sound pressure. If we double the power we see an extra 3dB... Link to comment Share on other sites More sharing options...
J Pearce Posted July 13, 2011 Share Posted July 13, 2011 Of course I did simon. I havent forgotten that SWL (not safe working load...) is 10log, I just slipped with my terminology. I can even remember all the reference values still. Link to comment Share on other sites More sharing options...
pete10uk Posted July 13, 2011 Share Posted July 13, 2011 All the math above is just gobbledegook to me. As J pearce mentioned in post 2, you can't beat what your ears are telling you. Link to comment Share on other sites More sharing options...
Simon Lewis Posted July 13, 2011 Share Posted July 13, 2011 All the math above is just gobbledegook to me.As J pearce mentioned in post 2, you can't beat what your ears are telling you. If anyone wants a simple explanation of the maths, I'm happy to help. (it's not like calculating inverse Z transforms!). I would suggest that understanding the published or measured figures is important, just as listening to the loudspeaker is important. We shouldn't buy or specify loudspeakers on figures alone, our ears should be the final arbiter. However, our ears can be quite easily fooled - they are not an objective tool - and it is possible for apparent loudness, fatigue or prejudice to cloud our judgement. That is when some properly measured hard figures can help... ! Link to comment Share on other sites More sharing options...
stevefez Posted July 13, 2011 Share Posted July 13, 2011 If anyone wants a simple explanation of the maths, I'm happy to help. Hi Simon, I would appreciate a simple explaination of the maths. I trust my ears explicity but would appreciate being able to understand the published figures besides the usual unreliable RMS/Peak figures... Link to comment Share on other sites More sharing options...
pete10uk Posted July 13, 2011 Share Posted July 13, 2011 If anyone wants a simple explanation of the maths, I'm happy to help. Hi Simon, I would appreciate a simple explaination of the maths. I trust my ears explicity but would appreciate being able to understand the published figures besides the usual unreliable RMS/Peak figures... Simon I would also appreciate some guidance on figures. Thanks for the kind offer. Cheers Link to comment Share on other sites More sharing options...
Simon Lewis Posted July 14, 2011 Share Posted July 14, 2011 OK... the issue is we want to know how good any loudspeaker is at converting the electrical signal from the amplifier into sound (its efficiency). To do this properly would require us to measure sound from the speaker in all directions. This is a bit of a pain to do, so to make it simpler, we measure just the sound level directly in front of the speaker, with the measurement mic placed 1m away and 1W applied to the speaker. This will give us a figure for loudspeaker sensitivity (i.e. it's different from efficiency, as we are only measuring in front of the speaker). If the speaker is good at converting the electrical signal into sound, then 1W might give us 105dB sound pressure. If it wasn't very sensitive, it might give only 90dB. The equation I referred to lets you work out the sound pressure a given speaker should produce. You take the loudspeaker sensitivity figure, and add to that ten times the log of the amplifier power that's being used. Let's try that for the example above... say we have a 30 W amp... you 'll need to work out logs, so just open calculator in Windows and key in 10 * 30 log = This gives 14.77 So, for a speaker with 90dB sensitivity, applying 30W gives us 90 + 14.77 = 104.77 which is near enough 105dB. For the 105dB sensitivity speaker 105 + 14.77 = 119.77 which is near enough 120dB. Years ago when we did use small 30W amps, this kind of increase in sensitivity made all the difference for cinema and public address speakers, and techniques such as horn loading would be used to increase sensitivity and get as much sound as possible. If we used more modern amplifier and speaker ratings, a 90dB speaker with a 1000W amp would give 90 + 10xlog1000 = 120dB, and the 105dB speaker would give 105 + 10xlog1000 = 135dB - a worthwhile improvement. The other parts we were discussing were to do with dB and how they are calculated. A decibel is simply ten times the log of the ratio of two powers. Let's say you have a 100W amp and you change it for one that's 200W. What is the power increase expressed in decibels? dB =10 x log (200/100) so dB = 10 x log 2, which is 10 x 0.3 = 3dB. So, doubling power gives us an extra 3dB. Now, what if we were looking at voltage or acoustic pressure? In both cases, power is proportional to the square of voltage or acoustic pressure. If we were comparing the increase in a circuit from 100 to 200 Volts, then we'd have to write it as follows: dB = 10log (200^2/100^2). Having to square each voltage is messy, so we take the square outside the brackets and multiply the 10 by 2. This gives us: dB = 20log(200/100), so dB = 20log 2, which is 20 x 0.3 = 6dB. Doubling the voltage in a circuit (I.e a gain of two) gives us an extra 6dB. If we are considering voltage or acoustic pressure, we use a 20log term. If it is power or acoustic intensity or acoustic power, we use 10log. I appreciate that this might still be a little heavy going, but once you have "got it" a lot of things (gain structure etc.) suddenly click into place... hope this helps, Simon besides the usual unreliable RMS/Peak figures... RMS is meant to be a reliable figure*, but the way it is measured (effectively what heating effect of an amp's sine wave signal can the speaker withstand?) isn't indicative of how we use loudspeakers. Unless one has unusual musical tastes, we don't listen to single frequency sine waves, and there is a much greater dynamic range in real music. The AES power rating uses band limited pink noise with a given crest factor and is usually a better indicator of what the speaker will handle in terms of music. There's quite a good article here if you want to read further... * Actually, many would argue that RMS watts is a misnomer, and we should refer to "average power".Peak can be specified closely, but PMPO etc. is veering into snake oil territory... Link to comment Share on other sites More sharing options...
Brian Posted July 14, 2011 Share Posted July 14, 2011 I will add a couple of thing to Simon's excellent post for those who want to go into more detail... 1) Speaker drive units suffer from something called 'power compression'. This is a figure, in dB, that you must subtract from your calculated maximum to give the real world figure. What happens is that as you drive a speaker hard bits heat up and other bits no longer work in a linear fashion. This means that the sensitivity of the speaker drops. A good driver will only suffer a drop of maybe 2dB; a bad driver might drop by as much as 6dB. Sadly, very few box makers give this figure and simply use the calculated maximum to state how 'loud' their box will go. 2) Don't underestimate the importance of sensitivity. Let's take Simon's example and look at it another way......a 90dB speaker with a 1000W amp would give 90 + 10xlog1000 = 120dB, and the 105dB speaker would give 105 + 10xlog1000 = 135dB... Suppose we only needed a 120dB. We could use the first set-up and achieve what we wanted. Or we could work out, using Simon's post, that with the second speaker we only need an amplifier capable of 120dB - 105dB = 15dB greater than 1W. Which is a antilog(15/10) * 1W = 32W amplifier. I know which I'd rather carry around. Link to comment Share on other sites More sharing options...
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