[vox-tech] Linux sound recording

Tue, 17 Jun 2003 10:33:12 -0700

Quoting Peter Jay Salzman <p@dirac.org>:

> On Tue 17 Jun 03,  8:36 AM, Henry House <hajhouse@houseag.com> said:
> > On Tue, Jun 17, 2003 at 08:15:19AM -0700, Peter Jay Salzman wrote:
> > > On Tue 17 Jun 03,  6:59 AM, Henry House <hajhouse@houseag.com> said:

[...]

> > Dumb newbie question: is a high signal-to-noise ratio (e.g., 100 dB)
> > better than a low one?
> 
> i think you want a high signal to noise ratio.   signal is considered
> good, noise is considered bad.

You betchum!

>   btw, human's can hear betwedn 1dB and
> 100dB.   a *really* noisy new york city subway train (like the IRT line
> in brooklyn) is about 120dB.  this is considered beyond the threshhold
> of pain.
> 
> decibels are on a logarithmic scale, meaning they're non-linear.   you
> would think that 3 dB is three times as loud as 1 dB, but it's actually
> ten times as loud.

I think you must have missed something here, pete... the factor is 2.

"deci" means one-tenth... the "bel" is "unit" (named after a certain inventor)
that represents a factor of ten ratio of power. It so happens that
log10(10)=1, so the ratio of "ten" corresponding to "one" bel suggests
the use of the logarithm base 10 in the equation:

  dB = 10 * log10( P / Preference )

We more commonly are able to measure amplitudes (with, say, a microphone and
an oscilloscope), and power increases with the square of the amplitude, so

  db = 10 * log10( (A/Areference)^2 )

or, rewritten using algebraic properties of logarithms,

  db = 20 * log10( A / Areference )

What is "loudness"?  If we assume it is the power in a sound wave, then
double the reference power gets us approximately 3 decibels.  Note that
"loudness" is not directly (linearly) related to the _amplitude_ of the sound
wave, so doubling amplitude yields a 6db change, but that is a fourfold
increase in _loudness_. [1]  Hoever, by neither interpretation can I see
where a tenfold increase comes from.

> decibels are units of power, but are used mostly for sound.  this is
> because the human ear's sensitivity is roughly logarithmic.   sound
> waves with power 1dB is roughly 10 times softer to a human than a sound
> wave with a power of 3dB.
> 
> btw, there are different definitions for decibels, but the differences
> are minor.  all definitions include a logarithm between two numbers you
> want to compare.
> 
> in practical terms, the range between the softest sound we can hear to
> the loudest sound we can hear without pain is roughly 12 orders of
> magnitude, so to an engineer, it's convenient to use a unit of
> measurement that's logarithmic, so they don't have to enter numbers like
> 124833.8742234 on their HP calculators.

Actually, it is because we don't like to spend effort multiplying, when the
same effect can be accomplished by adding and subtracting logarithms.
The number of decimals required to maintain accuracy actually nearly
doubles when using logarithmic scales... but addition is just so much
easier it is worth it.

>   kind of like how engineers use
> those stupid logarithmic bode plots that they learn in basic EE classes
> (but never use again) for transfer functions.

I have had to revisit those bode plots numerous times since I left school.
They are crucial in insuring that the equipment used to make measurements
doesn't contaminate data with measurement artifacts.
They also happen to be useful when defining "loudness", since the
hearing process has a "signal transfer function" that affects our
perception of "loudness" depending on the frequency involved. This gets
particularly complicated when listening to "normal" sounds that are not
pure single-frequency sounds, but the math still serves as a practical
model that computers can evaluate if needed.

> of course, to a physicist, decibels are inconvenient, because to us,
> everything has a power of "P".    ;-)

Well, we are on your home turf _here_. *whizzz* (what was that?)

[1] http://www.phys.unsw.edu.au/music/dB.html

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