A Question on Speaker Driver Efficiency

For a single driver : The change in dB in input voltage is equal to the change in output SPL in dB.

Voltage dB can be calculated in this fashion: 

dB = 20 x log ( Vnew / Vold )

in the case of half the voltage:

20 x log ( 1 / 2 ) ~= (- 6 dB)

Also, you can use this handy web gizmo:

http://www.sengpielaudio.com/calculator-gainloss.htm

Also, we are so far from the OP's original topic, maybe we should let this thread just die. :) 

@cj1965 and other Respected and Valued contributors to this forum. cj1965 is obviously well schooled in the math, a stickler for precision, and interested in the truth of the matter. I believe/hope his knowledge “could” become valued here. However, “manners” are vital in order to become a “respected and Valued” member of any reasonable group. “Anyone” can have a misstep or slip up. We’re human. Such an event “does not” necessarily diminish one’s value or credibility. I’ll mention Ralph here as he is known to produce exceptionally listenable and prized audio equipment under the ATMASPHERE label; and is without doubt a valued contributor. 
However, harsh criticism, or sarcasm, is “generally recognized” as a deliberate attempt to demean a person.
Reasonable and compassionate people will/may react to defend the person(s) subject to the personal attacks. 
This has occurred here. 
I don’t support a ban of the offender at this time. He may have been having a “bad day(s) for reasons unknown. I do believe apologies are “generally accepted”; and are a good response to a correction of a error in a “statements of fact”, even if semantics are causing the misunderstanding, as well as for “personal insults”. Unfortunately, insults are more unacceptable than factual errors(which can always be corrected!). Insults, even if based on accurate facts, cannot be corrected. They linger in the minds of all. I highly recommend the high road of, at the minimum, a general apology for insulting comments. And best wishes to all. Peter

@erik_squires 

No, we're not far off from the essence of the question posed by the OP. Application of the decibel expression of voltage gain/loss to sound power gain/loss is not appropriate..

Sound power level, denoted LW and measured in dB, is defined by

LW = 10 log 10 ( P/P 0 )   d B

not 20 X log 10(P/Po) db as you suggested above.

 

... not 20 X log 10(P/Po) db as you [Erik] suggested above.

CJ1965, Erik did not say that or suggest that.

He said 20 x the logarithm of the ratio of applied voltage, not 20 x the logarithm of the ratio of power. If half the voltage is applied power will be reduced to 1/4 of the original amount, resulting in a 6 db reduction in SPL according to your own 10log(P/Po) formula, which is correct. And that is what Kijanki was implicitly pointing out when he quoted your erroneous original comment on the matter.

Also, and more significantly, +1 to the very well said comments above by Peter (Ptss), which together with the earlier comments by Timlub I suggest that you (CJ1965) would be well advised to take to heart.

Regards,
-- Al