I can’t figure this all out, and we’re becoming convinced that the book we’re using has a misprint. What I think I need is a table. Can you complete this table?
Reference level ___ bel
1 bel ___ x louder ____ x more energy
2 bel ___ x louder ____ x more energy
3 bel ___ x louder ____ x more energy
4 bel ___ x louder ____ x more energy
Just for further info/checking:
1 db ___ x louder ____ x more energy
2 db ___ x louder ____ x more energy
3 db ___ x louder ____ x more energy
4 db ___ x louder ____ x more energy
It’s important to understand that dB isn’t a measure of loudness, which is a largely subjective quantity. As it applies to sound, dB is normally used to express sound pressure level, although there are several weighting schemes which attempt to approximate sound level by compensating for the frequency response of the human ear. The reference level for 0 dB, the baseline level, is normally the threshold of hearing for the average human ear, which is a SPL of 20 microPascals, a quantity that Wiki states is about the same as the sound of a mosquito from 3 feet distant. Every 3 dB represents a doubling of this level; every 10 dB is an increase of one order of magnitude.
But everything else I’ve read says that a 2 bel increase is a 10 fold increase in intensity, while “sounding” twice as loud. How then does a 3 bel increase have 1000 times the original energy? I can’t reconcile this, and neither could my MIT engineer dad.
This also seems to back up my understanding. If the factor of 1000 is really supposed to be 100, then it’s about the fifth error we’ve found in this, and things start to make sense.
Maybe you’re confusing amplitude and energy? Energy is proportional to square of amplitude. A 1-bel increase is a 10-fold increase in energy, which means a sqrt(10)=3.1 fold increase in amplitude. A 2-bel increase is a 100-fold increase in energy, or 10-fold increase in amplitude. A 3-bel increase is a 1000-fold increase in energy, or sqrt(1000)=31 fold increase in amplitude.
This starts to approach the table I asked for. This starts to work. What is still confusing is that 2 bels is supposed to be twice as loud. What then is the perceived loudness increase at 1 bel increase in intensity/energy?
And (yes, I’m complaining), I think all this back and forth could have been solved if someone would have just filled in a bit of the table I asked for. Just throwing quotes in from other web pages and so on not only isn’t what was asked for, it’s kind of implying that if I’d just do some extremely simple research, it would be obvious. I think I implied even in the OP that I’m not just running here first because I want someone else to do my thinking for me.
Close, but not quite. Bels and decibels are used to work with power ratios, rather than energy. For example, since decibels are most common in sound, lets use a real world example. The JBL Vertec V4889 is a loudspeaker you will commonly see when you go to see large arena & stadium concerts. It is a 3-way speaker, needing separate amplifiers for low, mid, and high frequencies. The low frequency section has a rating of 99 dB @ 1 W/1 m. What this means is that when you give the low frequency section of the speaker 1 W, you will measure an unweighted SPL of 99 dB 1 meter away from the speaker. Now, I’ll fill in you’re chart starting with this information
1 W=99 dB SPL
2 W=105 dB SPL = 2 x the power = 2 x as loud = +6 dB = +.6 Bel
4 W=111 dB SPL = 4 x the power = 4 x as loud = +12 dB = +1.2 Bel
8 W=117 dB SPL = 8 x the power = 8 x as loud = +18 dB = +1.8 Bel
So, you can see that an increase of 1 Bel (10 dB) gets you approximately 4 times the power and 4 times the loudness, while an increase of 2 Bel (20 dB) is approximately 8 times the power and 8 times the loudness.
I don’t deal in sound levels too often, but I deal in dB measurements all day every day. A few points:
I never see anyone use bels, never. It’s always dB.
I don’t know what the phrase “sounds like it’s twice as loud” means. I can’t imagine any context in which that would be meaningful.
The ratios are for power, not energy.
People here have been throwing around the terms intensity (amplitude) and power - these are different. Power goes up with the square of the amplitude, therefore a 20 dB increase is 10x the amplitude and 100x the power.
In your chart, you ask for how many times louder, but what do you mean by that? Are you referring to amplitude? If so, here are your answers:
Reference level ___ bel
1 bel 3 x [del]louder[/del] amplitude ____ 10 x more [del]energy[/del] power
2 bel 10x [del]louder[/del] amplitude____ 100 x more [del]energy[/del] power
3 bel 30x [del]louder[/del] amplitude____ 1000 x more [del]energy[/del] power
4 bel 100x [del]louder[/del] amplitude____ 10000 x more [del]energy[/del] power
Just for further info/checking:
1 db 1.12 x [del]louder[/del] amplitude 1.26 x more [del]energy[/del] power
2 db 1.26 x [del]louder[/del] amplitude 1.58 x more [del]energy[/del] power
3 db 1.41 x [del]louder[/del] amplitude 2.00 x more [del]energy[/del] power
4 db 1.58 x [del]louder[/del] amplitude 2.51 x more [del]energy[/del] power
“Louder” probably refers to something with the physiology of human perception of sound. I know that human vision works on an approximately logarithmic response scale, and I’m pretty sure that hearing does, too. That’s why we use decibels to measure loudness in the first place, rather than some linear unit. But of course, it’s very difficult to quantitatively assess human response to stimuli, so any figure you see for how loud something “seems” will be somewhat fuzzy.
I know we usually use dB, but these students have never seen this stuff, so I’m starting at the fundamental level. Plus, the math for dB is kind of confusing, as a 3dB increase is more like a doubling in power.
I know dB is based on power, but since the time isn’t changing, it must be the energy component of the Watt that’s changing. I didn’t know that about the amplitude. This book is focusing on sound waves specifically, and so is making points about human perceived loudness.
If I can ask for more, can someone explain how the amplitude supplied by CurtC is relating to the power increases? 3x amplitude is 10x power?
I have no idea what you’re saying. Getting back to the point of how dBs talk about power ratios, not energy ratios, it would be like asking “how much faster is 40 miles compared to 20 miles?” Those aren’t speeds, they’re distances.
My thinking was that if someone put me in a test lab and asked me to say when one sound was “twice as loud” as another, I would be completely baffled about what he wants me to do. No human can do this, and if you ask a set of random people to give you that information, they’ll either be making stuff up or applying some misunderstanding of their perception to pick an incorrect answer.
Sound is just a wave of air pressure changes, the molecules move back-and-forth between the source and the listener, propagating the wave. If you start with a bigger stimulus that causes the molecules to move twice as much as they did before, that is what’s referred to as twice the amplitude. If you measure the power transmitted by this, it will be four times as much. Power of a wave is proportional to the square of the amplitude. To answer your question, if a signal has ten times the power of another signal (10 dB more), then the amplitude ratio will be the square root of ten, 3.16 - about three.
What I was saying is that the distance-speed analogy fits this perfectly. If someone asks how much faster is 40 miles compared to 20 miles, what do you say? Maybe to him, he’s assuming you cover those distances in the same amount of time, therefore he’s thinking the answer is “twice as much.” But that’s a pretty sloppy and ambiguous way to express it.
You made the assumption that “the seconds aren’t changing.” Why? What is that from? We’re comparing ratios of power levels, not energy.