A Question on Speaker Driver Efficiency

Double check the sensitivity on each! :) It is very unusual that the same driver has the same sensitivity regardless of impedance! It's not impossible, but usually manufacturers cut the sensitivity by 3dB as impedance doubles. 

Yes, your math is correct.  Again, I encourage you to grab XSim Crossover Simulator for PC or equivalent to try these ideas out. 

Best,

E

If the amp puts out x watts at 8 ohms, and you split it between two speakers totalling 8 ohms, each speaker sees the half the power and puts out the same dB level.  When you add them together, the net result is the same.

That said, I would think that, if the net volume in dB for the speakers truly are the same regardless of the impedience, two 16 ohms speakers would be the better choice.

Speakers in parallel work independent of each other.  Speakers in series work together and can have an effect on each other.

Also, speakers with higher impedience tend to have a high Bl, and therefore follow the signal more accurately.

@toddalin - what is -  "high Bl"

Thanks

Placing woofers in series will double the resistance and inductance.  This will cause a more steep frequency response roll off on the upper end and will show how sensitive the drivers are at half their standard drive level sensitivity rating. In theory, half the voltage applied to a driver will result in half the sound pressure in the output (-3db). But if two drivers outputs are combined, in theory, output should be doubled - thus cancelling out the effect that halving the applied voltage generates. That's the theory. In practice, the summation of separate but identical woofer responses is somewhat complicated because the way sound pressure waves combine in free space depends largely on the size of each sound source relative to the frequency wavelengths of interest, the relative proximity of the sources in space to one another, and the location in space that response is being detected. In general, you will find that the parallel/series arrangement of multiple drivers can improve overall acoustic efficiency and "apparent sensitivity" at lower frequencies. The essential reason for this is that more driver surface area improves acoustic coupling of the energy source (voltage) to the media being acted upon (air molecules). Try connecting four identical woofers with two series pairs in parallel. You should witness increased output at low frequencies over a single driver for the same applied voltage at most voltage levels Again, however, what is detected in response is heavily dependent on the spatial and frequency characteristics outlined above. Electrically, you should have the same nominal net impedance as one driver but acoustical coupling improvements should provide increased output for the same applied voltage and current draw (the series/parallel arrangement of the 4 woofers should restore the net final inductance value to approximately that of one woofer). All of the above ignores issues pertaining to  the driver's inherent non linearity caused by electrical/mechanical energy loss/storage. For the purposes of the above explanation, one should just assume a "linear" driver.

" If the amp puts out x watts at 8 ohms, and you split it between two speakers totalling 8 ohms, each speaker sees the half the power and puts out the same dB level. When you add them together, the net result is the same.

That said, I would think that, if the net volume in dB for the speakers truly are the same regardless of the impedience, two 16 ohms speakers would be the better choice.

Speakers in parallel work independent of each other. Speakers in series work together and can have an effect on each other.

Also, speakers with higher impedience tend to have a high Bl, and therefore follow the signal more accurately. " -toddalin

I'm afraid very little of what toddalin said above is true. Loudspeaker drivers don't "divide up" power. They respond to a driving force we call voltage. Placing them in series means that voltage is divided between them. Placing them in parallel means that voltage is shared. In the former case, the current drawn from the source is cut in half. In the case of the latter, current drawn from the source is doubled. Sensitivity is professionally expressed as acoustic output generated (typically at one meter distance) for 2.83 Volt RMS input.  It is not expressed in acoustic output (db) per watt of input. That technically, is a measure of efficiency - not sensitivity. With 2.83 Volts applied to two identical drivers in parallel, sensitivity is nearly doubled - BUT SO IS THE CURRENT DRAWN. So there's no net improvement in EFFICIENCY. With two identical drivers in series, current is cut in half because resistance is doubled. Sensitivity may be marginally reduced or improved depending on the sensitivity curve of the driver (how linear the driver's output changes with changes in drive level)

As for the 16 ohm explanation toddalin provided - it is completely bupkiss. A loudspeaker's force factor has nothing to do with its electrical impedance. Force factor is the force exerted on a voice coil that is traversing a magnetic field. A 16 ohm resistance voice coil can have the same force factor curve as a 4 ohm voice coil. Voice coil resistance is not an accurate predictor of driver non linearity (accuracy).