I add 3 db to the number obtained from High Fidelity's graph, and the
resulting number turns out to represent with pretty fair accuracy the sound pressure level (SPL) obtained at an average location in a room
o f 2 0 0 0 - c u b i c - f e e t v o l u m e a n d m o d e r a t e l y l i v e a c o u s t i c s , f o r a o n e - w a t t i n p u t . Then, knowing the SPL produced by one watt of amplifier
p o w e r , t h e p o w e r r e q u i r e d t o p r o d u c e a s o u n d l e v e l o f 1 0 0 d b c a n b e c a l c u l a t e d f r o m t h e e q u a t i o n : P = antilog ( 100 - SPL).
(2) Consumer's Union, whose reports on high-fidelity gear have to be taken with a grain of salt in some respects, do include in their loudspeaker evaluations a "required power" figure which can be taken
as an indication of relative speaker efficiency.
CU do not specify how
their power figures are obtained, but I find that doubling their numbers gives results which agree roughly with the power figure for 100 db which
I derive from
(3) Estimates of relative efficiency can be obtained from compara- tive listening tests in showrooms or at home, but great care must be taken. If 8-ohm and 4-ohm speakers are compared and sound equally loud at the same volume control setting (or at the same reading on an amplifier's "power" meter), the lower-impedance speaker is actually absorbing more power and so is about 3 db less efficient. If equally efficient 8-ohm and 4-ohm speakers are compared, the 4-ohm speaker will sound louder at the same volume control setting. Another problem with listening comparisons is that a speaker with an upper-midrange peak will sound subjectively loud and so more efficient than it really is.
( 4 ) M o s t l o u d s p e a k e r s o b e y a p h y s i c a l r e l a t i o n s h i p b e t w e e n l o w - T h i s r e l a t i o n s h i p frequency response, cabinet size, and efficiency.
was established about 15 years ago at Acoustic Research; Henry Kloss
calls it Hoffman's Iron Law. It doesn't apply to speakers which contain
"acoustic amplification," such as the Klipschorn and Heil's air motion transformer, but it does apply generally to closed-box loudspeaker systems. In a form practical for calculations it can be expressed as:
Here E is the efficiency of the woofer in the frequency region where its
response is flat; the efficiency is expressed as a percentage, and though the formula gives only the woofer's efficiency the tweeter's efficiency obviously will be matched to the woofer if the speaker sounds good. The V in the formula is the effective volume of the cabinet, in cubic feet. F is the resonant frequency of the woofer as mounted in the box (not the free-air resonance). Q is the reactance/resistance ratio at resonance; in practical terms it may be taken as a number which specifies the shape of the speaker's low-frequency response. A speaker with a Q of about 1 is approximately flat down to the resonant frequency. A Q much higher than one would mean a pronounced peak at resonance; with a Q of less than 0.8 the speaker's low end would start rolling off at about twice the resonant frequency. Many good speakers have a Q of about one. The equation indicates that such a speaker, with a resonant
frequency of 45 Hz in a 2 cubic foot box will have an efficiency of about 1% (or worse if the design is not optimum). At that efficiency a speaker will produce a sound level of about 84 db at 1-watt input, in an average room.