From: Ronald Wong (ronwong@inreach.com)
Date: Thu Jan 16 2003 - 01:28:45 PST
Message-Id: <l03102802ba4ae2c2af68@[209.209.19.163]> Date: Thu, 16 Jan 2003 01:28:45 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: Decibel ratings on tuners
Recently Nathania Chaney Aiello said:
>I have been teaching sound to my AP Physics students and discussing that
>loudness is a perception based on the intensity of the wave. I indicated
>that the decibel scale was designed so that 0 was the threshold of human
>hearing and positive numbers were used for sound that humans (on average)
>could hear. So today, a sharp kid brings in the specs for his stereo
>receiver and it has a range of "-60 to 0 to 18 dB, in steps of 1 dB." How
>is this possible? What is this 0 based on and how can it be reading negative
>numbers?
Nathania:
The decibel scale that you are referring to is based on the log of the
ratio of the intensity of a particular sound to the intensity of sound at
the threshold of hearing. The latter occurs when one pJ (1 pico-joule = 10
to the negative 12th joules = 10^-12 J) of sound energy passes though (or
falls on) a square meter every second.
When it comes to the intensity of sound, it turns out that we respond to
different levels of intensity in a logarithmic way rather than a linear
way. This allows us to sense a very wide range of intensities. To express
this fact in a meaningful way we compare the intensity of a given sound to
some arbitrarily chosen point of reference (the threshold of hearing for
instance) and take the log of that ratio. The result is the intensity level
(NOT the intensity) and is measured in bels.
Since a difference of 1 bel covers a noticeable difference in our sense of
the sound level's change in intensity, we use a smaller unit - the decibel
(db). As a result, the equation for the intensity level is usually written
as:
db = 10 * log(I/Iref) where Iref is 10^-12 W/m^2, the threshold of hearing.
When it comes to logarithmic functions it's important to remember that the
log of any number greater than one is positive. When the number is equal to
one, it is zero. When it is less than one, it is negative. The reason for
this becomes apparent if you remember that the log is just the power to
which the number 10 has to be raised in order to get the value that you are
taking the log of.
For instance, the log of 10 is 1 because 10 to the first power is 1. The
log of 1 is zero because 10 to the zero power is 1. The log of 0.1 is -1
because 10 to the negative one is one-tenth and one-tenth is 0.10.
A source of sound which is 10 times greater in intensity than that of the
threshold of hearing (i.e. I = 10^-11 W/m^2) would have a bel rating of
exactly 1 (which is 10 decibels). A source of sound that is 10 times lower
in intensity than that of the threshold of hearing (i.e. I = 10^-13 W/m^2)
would be one tenth of the threshold of hearing and would have a bel rating
of -1 (or -10 decibels).
Although you can't hear sound when it's intensity level is negative, such
levels of sound do exist and scientists go about measuring them just like
they go about measuring everything else that they can get their hands on.
It was interesting to read Mark's and Al's remarks regarding your question
about the range of levels from -60 to 18 db.
When you see the specifications for a tuner where decibels are involved,
the values are usually positive, negative or both. In the last case the two
values are usually centered about 0 db. I've never seen one as asymmetrical
as the range you referred to and have never seen one with a value as low as
-60 db (but then I haven't seen everything - yet).
So, instead of giving you an explanation based on electrical properties, as
Al and Mark did, I'll take a stab at one that involves sound.
The fact is you never stated what "it" was that had a range of -60 db to 18
db,
If "it" involved the volume control and the -60 db is the lowest setting on
the dial - at which point you find that you can't hear anything - then the
manufacturer of the receiver probably used a different value for Iref then
the conventional one. Instead of comparing the level of sound intensity to
10^-12 W/m^2 (the threshold of hearing), s/he used 10^-6 W/m^2 (approx. the
level of an ordinary conversation).
With that as a point of reference, -60 db would be at the threshold of
hearing, 0 db would be at a the "conversational" level (the "normal" level
of sound for the receiver), and the 18 decibels would be at the level of a
very noisy train ("loud") - normally, 18 db would be around the level of a
whisper.
Just a thought.
ron
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