Decibel vs. Bel
sane54
(p1/p0) and be one tenth of a bel at the same time? I've checked in
like three places, including the Yamaha Sound Reinforcement and
Wikipedia entry and they all define decibel as one tenth of a Bel and
yet show the mathematical formula as ten times a Bel. No amount of
logarithm math seems to work. What's going on? What am I missing?
Les Cargill
It is *ONE TENTH* a Bel.
You are welcome.
--
Les Cargill
Soundhaspriority
"sane54" <san...@sane54.com> wrote in message
news:d31ca732-766f-425c...@l30g2000yqb.googlegroups.com...
Sane,
This is the error. When they say a level of loudness of 1 Bel is 10X
that of a level of 1 dB, they are correct. But logarithms exist for use with
logarithmic identities, not standard math operations.
The wrong way to look at it is this: Bel = 10*Decibel . We need to work with
these as exponents. So,
The right way to look at it is 10^Bel = 10*10^Decibel, which =
10^(Decibel+1)
Or, you could write
log(10^Bel) = log( 10 * 10^Decibel )
Bel*log(10) = log(10) + log( 10^Decibel)
But since log(10) = 1,
Bel = 1 + Decibel*log(10) = 1 + Decibel
Hope this helps,
Bob Morein
(310) 237-6511
John O'Flaherty
wrote:
If you have $1, you have one hundred pennies. So, the number of
pennies is 10 times the number of dollars, because the pennies have
1/10 the value of a dollar.
If you have one bel, you have ten decibels. So the number of decibels
is 10 times the number of bels, because the decibels have 1/10 the
value of a bel.
--
John
Don Pearce
Is everybody still drunk from new year?
d
George's Pro Sound Co.
"Don Pearce" <sp...@spam.com> wrote in message
news:4b42d972....@news.eternal-september.org...
no this is just obamanomics
George
Mike Rivers
> If you have $1, you have one hundred pennies. So, the number of
> pennies is 10 times the number of dollars, because the pennies have
> 1/10 the value of a dollar.
Did you buy those pennies on eBay?
--
"Today's production equipment is IT based and cannot be operated without
a passing knowledge of computing, although it seems that it can be
operated without a passing knowledge of audio." - John Watkinson
Jens Rodrigo
Here is a nice calculator bel to dB and decibel to bel an more...
http://www.sengpielaudio.com/ConvBel.htm
Cheers Jens
John O'Flaherty
wrote:
>John O'Flaherty wrote:
>
>> If you have $1, you have one hundred pennies. So, the number of
>> pennies is 10 times the number of dollars, because the pennies have
>> 1/10 the value of a dollar.
>
>Did you buy those pennies on eBay?
Yike! And the question wasn't even about centibels!
--
John
sane54
I appreciate all the responses - I like Bob's the best. I'm still not
entirely satisfied though. Bel is defined as the base 10 log of a
ratio of two powers. The decibel formula is ten times the log of a
ratio of two powers. If I substitute those into Bob's equation then I
get log(p1/P0) = 1 + 10 * log(P1/P0) which is nonsense.So one or the
other definition is wrong. We use 10 * log(p1/p0) all the time, but
presumably Bel came first and is a more intuitive definition.
Bob Eld
"sane54" <san...@sane54.com> wrote in message
news:d31ca732-766f-425c...@l30g2000yqb.googlegroups.com...
Because there are 10 times as many decibels as bels. In other words the
number of units in dB's is 10 times bigger than the number of units of bels.
Its just like 1$ = 10 dimes. There are 10 times as many dimes as dollars
even though each dime is 1/10 of a dollar. You are confusing the number of
units with the value of each unit.
Le...@nospam.com
I think your mistake is to say "a bel" is log (p1/p2)...
You shoud say "number of Bels" is log (p1/p2)...
So in a ratio of 2 to 1, you have :
bels = log ( 2/1) = 0.3
and in decibels you would have
decibels = 10 * log ( 2/1 ) = 3
3 decibels is 0.3 bels...
William Sommerwerck
> ie 10 log (p1/p0) and be one tenth of a bel at the same time?
Because they're exactly the same thing!
A quarter is one fourth of a dollar -- and there are four quarters in a
dollar.
Misifus
The bel came first, but was immediately perceived to be of limited
practical use. Thus, the decibel (literally a tenth of a bel) came into
being and has essentially displaced the bel as a useful unit of measurement.
-Raf
--
Misifus-
Rafael Seibert
Photos: http://www.flickr.com/photos/rafiii
home: http://www.rafandsioux.com
Misifus
Well said.
sane54
>
> - Show quoted text -
Ahh ok the Bel is considered a fundamental unit of measure - so
therefore:
log (p1/p0) * (1 Bel) = 10 * 1/10 log (p1/p0) * (1 Bel) = 10 * log (p1/
p0) * (1/10th of a Bel) = 10 * log(p1/p0) * (1 dB)
I got it. I think. I'm still a little shaky on what a Bel actually
IS.
Jim Lacey
>> - Show quoted text -
>
>Ahh ok the Bel is considered a fundamental unit of measure - so
>therefore:
>
>log (p1/p0) * (1 Bel) = 10 * 1/10 log (p1/p0) * (1 Bel) = 10 * log (p1/
>p0) * (1/10th of a Bel) = 10 * log(p1/p0) * (1 dB)
>
>I got it. I think. I'm still a little shaky on what a Bel actually
>IS.
At the time the Bel was specified it was the attenuation produced by
a mile of standard telephone cable to the audio signals then in use
for telephony.
As stated by a previous poster it was too large for normal purposes so
a tenth of a Bel was adopted instead.
Jim Lacey
sane54
Thanks everyone. It's all clear to me now.
Jim Lacey
On Thu, 7 Jan 2010 15:53:13 -0800 (PST), sane54 <san...@sane54.com>
wrote:
>On Jan 7, 11:28�am, Jim Lacey <bo...@virgin.com> wrote:
Is that as clear as a Bell?
Jim
Arkansan Raider
It certainly rings true for me.
---Jeff