Re: loudness and dB

[Dave Keenan, TD 189.1:]
> a doubling of amplitude is not "twice as loud" but only 6dB louder,

OK, no one else followed up on this, so I will. It is my understanding
that a wave of twice the amplitude will produce four times the energy
(energy being proportional to the square of amplitude).

A "Bell" represents 10 times the energy, and therefore 6dB represents
10 ^ 0.6 = 3.98 times the energy; it is used as shorthand for 4.0 times
the energy, just as 3dB is shorthand for double energy.

Yes? No?

[Jeff Scott TD 189.14:]
> Sorry, that was just a brain fart on my part. I meant twice the
> amplitude. And I think it would actually be 3dB since it is a single
> pole filter. 2x amplitude = +6dB amplitude = +3dB power.

I think you were closer to right the first time!

> (perceived "loudness" curves are related to power intensity though
> not the same).

Is that the real issue here? If so, does it really mean anything to
speak of "twice as loud"? And how many dB would that be?

JdL

Yes, John, you're right. Just one small nit. Usually, one usually uses
dB with units of power (Watts), not energy (Joules = Watts x seconds).

2x amplitude = +6dB amplitude = +6dB power = 4x power.

Fred Reingel

John A. deLaubenfels wrote:
>
> From: "John A. deLaubenfels" <jadl@idcomm.com>
>
> [Dave Keenan, TD 189.1:]
> > a doubling of amplitude is not "twice as loud" but only 6dB louder,
>
> OK, no one else followed up on this, so I will. It is my understanding
> that a wave of twice the amplitude will produce four times the energy
> (energy being proportional to the square of amplitude).
>
> A "Bell" represents 10 times the energy, and therefore 6dB represents
> 10 ^ 0.6 = 3.98 times the energy; it is used as shorthand for 4.0 times
> the energy, just as 3dB is shorthand for double energy.
>
> Yes? No?
>
> [Jeff Scott TD 189.14:]
> > Sorry, that was just a brain fart on my part. I meant twice the
> > amplitude. And I think it would actually be 3dB since it is a single
> > pole filter. 2x amplitude = +6dB amplitude = +3dB power.
>
> I think you were closer to right the first time!
>
> > (perceived "loudness" curves are related to power intensity though
> > not the same).
>
> Is that the real issue here? If so, does it really mean anything to
> speak of "twice as loud"? And how many dB would that be?
>
> JdL
>
>

[John A. deLaubenfels TD 196.4]

>[Dave Keenan, TD 189.1:]
>> a doubling of amplitude is not "twice as loud" but only 6dB louder,
>
>OK, no one else followed up on this, so I will. It is my understanding
>that a wave of twice the amplitude will produce four times the energy
>(energy being proportional to the square of amplitude).

Thanks John. Sorry I didn't follow it up myself. I was afraid of being seen
as the pedant that I am. You're right, except strictly speaking, it is
power, not energy. Power being energy per unit time.

>A "Bell" represents 10 times the energy, and therefore 6dB represents
>10 ^ 0.6 = 3.98 times the energy; it is used as shorthand for 4.0 times
>the energy, just as 3dB is shorthand for double energy.
>
>Yes? No?

Yes indeed (with the above modification).

>[Jeff Scott TD 189.14:]
>> Sorry, that was just a brain fart on my part. I meant twice the
>> amplitude. And I think it would actually be 3dB since it is a single
>> pole filter. 2x amplitude = +6dB amplitude = +3dB power.
>
>I think you were closer to right the first time!

Yes. It's not a single-pole filter and, as Fred Reinagel wrote [TD 196.6]

2x amplitude = +6dB amplitude = +6dB power = 4x power.

dB is defined as 10*log_10(Power ratio) or 20*log_10(Amplitude ratio) so it
gives the same number irrespective of whether it is based on amplitude or
power.

>> (perceived "loudness" curves are related to power intensity though
>> not the same).

Just referred to some standard sound pressure amplitude, or acoustic power
per unit area, as being 0dB (just inaudible) and weighted lower for the
high and low frequencies.

>Is that the real issue here? If so, does it really mean anything to
>speak of "twice as loud"? And how many dB would that be?

Yes I think it is the issue and it makes sense to speak of twice as loud.
It's not a fixed number of dB. Twice as loud is just twice as many dB
(approximately).

Regards,
-- Dave Keenan
http://dkeenan.com

[me, TD 196.4:]
>>It is my understanding that a wave of twice the amplitude will produce
>>four times the energy (energy being proportional to the square of
>>amplitude).

[Dave Keenan, TD 197.10:]
> You're right, except strictly speaking, it is power, not energy. Power
> being energy per unit time.

Quite correct; I was zoned out...

[me, regarding perceived loudness:]
>>Is that the real issue here? If so, does it really mean anything to
>>speak of "twice as loud"? And how many dB would that be?

> Yes I think it is the issue and it makes sense to speak of twice as
> loud. It's not a fixed number of dB. Twice as loud is just twice as
> many dB (approximately).

No kidding? That surprises me! Does anyone have references to studies
done on perceived loudness that you could point me to?

JdL