# HOW TO UNDERSTAND DIFFERENT IMPEDANCE RATES?!!!

John Woodgate jmw at jmwa.demon.co.uk
Mon Jun 9 02:03:29 EST 1997

```In article <33b12876.20360271 at news.pacbell.net>, God <god at almighty.com>
writes
>The original fallacy:
>
>>Consider an amplifier with an 8 ohm output impedance feeding 8 volts into
>>a speaker with an 8 ohm impedance.  The speaker will be dissipating 8
>>watts of power and will generate a specific sound pressure level.
>>
>>Next, consider the same amplifier putting 8 volts into a 16 ohm load.
>>Since P = E^2 / R, the power being pumped into the load is 8^2 / 16, or 4
>>watts, which will yield a lower sound pressure level.
>>
>>The assumption, of course, is that both speakers have the same efficiency
>>and are, in fact, identical except for their impedances.
>
>1) An amp driving 8 volts into 8 ohms will dissipate 8 W of power and
>an SPL of  A.
>2) An amp driving 8 volts into a 16 ohm load will dissipate 4W of
>power and an SPL of  >A.

You really are a most unsatisfactory god, you know (of course you
know!). If this goes on I shall have to stop worshipping you, and then
where will you be? You have the inequality sign the wrong way round; at
least, I suppose you did not mean 'greater than'!

>3) We assume that both "speakers" in 1) and 2) have the same
>efficiency (and identical except for their impedances.)

Yes, the following reasoning is correct if, and only if, you mean
efficiency in the strict sense of sound power out divided by electrical
power in, but hardly anybody uses that because it is difficult to
measure and not of great practical use.

>4) Ergo, a 16 ohm speaker is less sensitive than an 8 ohm because at
>the same WATTAGE, the former produces a lower SPL ** from 1) and 2)
>
>He did prove his
>point that the higher impedance speaker would produce lower SPL at a
>given voltage. However, when he translated this to lower SPL at a
>given wattage, he committed the fallacy of four terms, a non sequitur
>fallacy of ambiguity.

If by 'he', you mean me (John Woodgate), I certainly did not 'translate
that to a lower SPL at a given power' (I would even more certainly not
have written 'wattage' - ugh!). I fail to disceren any meaning at all in
the phrase 'a non sequitur fallacy of ambiguity'. A non sequitur is
false reasoning - the conclusion 'does not follow' from the premise(s).
An ambiguity is a language-dependent construct - what is ambiguous in
one language may not be in another (e.g. if the ambiguity arises from a
pair of homophones).
>
>If you still insist that the fallacy is petitio principii, please tell
>us DIRECTLY where this occurs.
>
>>>Apparently, you are a little disgruntled because you incorrectly
>>>identified a petitio principii.
>>
>>Being a god, you' know that of course, even if I deny both your
>
>Well, if you don't want people to infer that, make it less obvious.
>And I never claimed to be god.
>
>> Just becuase you know the Latin name for
>>something does not mean that you could see one if it bit you.
>
>Well, if  little flees bit your glutei maximi, you wouldn't be able to
>see it either.
>
>>The
>>article in question assumed sensitivity was inversely related to
>>impedance and then proved it from the same starting point. That 'begs
>>the question',without doubt.
>

If one says that 'the loudspeakers are identical except for their
impedance' (whether 'efficiency' is mentioned explicitly or not), that
is indeed a statement in which it is inherent that sensitivity,
correctly expressed as pascals per volt (these are quantities of the
same nature, known as 'field quantities', which can rigorously be
presented as a ratio), is inversely proportional to impedance. That is
where the question was begged - it applies ONLY to transducers that are
identical except for impedance.
>
>>>But let me quote you:
>>>"If the reference efficiency, ho, is unknown, it can be accurately
>>>calculated from the sensitivity if the sensitivity is referenced to 1
>>>watt." -- JBL Speaker Shop help file
>>
>>Not that alone, you need the directivity index as well. Maybe that was
>
>Then how on earth can the software ACCURATELY calculate the reference
>efficiency from the sensitivity referenced to 1 watt. As far as I
>know, JBL speaker shop does not have a random number generator for its
>speaker parameters.

Wanna bet? (;-) Why not ask JBL how they do it? I suspect they include
the directivity index without telling you.
>
>>Quoting manufacturer's literature as a technical authority shows extreme
>>naivety. The 'sensitivity' quantities that have been mentioned are all
>>dimensioned quantities. Efficiency is a pure ratio, and dimensionless.
>
>Christ, not for practical purposes. Force is a vector quantity, but we
>don't say "this object has 450N, in the direction of the center of the
>earth."

Well either you want a proper technical discussion, in which precision
is necessary, or you want a thread full of folk-lore and hand-waving. If
the latter, I will not join you.
>
>> You call making unjustified assumptions about people's
>>motives for posting 'courtesy'?
>
>What other motive can you offer for why your response was so rude? Is

Oh, dear, accused of blasphemy, now! Peccavi. Mea culpa. Mea maxima
culpa.

If you think what I wrote was rude, you are very inexperienced in
Abusenet! However, I did not intend to be rude, and if you feel that
something I wrote was rude, I regret that. My intention is only to
hinder the propagation of factually incorrect information.
--
Regards, John Woodgate Tel. +44 (0)1268 747839
Fax +44 (0)1268 777124. OOO - Own Opinions Only
Alternative e-mail address: jmwa at thenet.co.uk
That means I get double spam with everything (;-(

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