Simple driver SPL equation needed

[taj]

What is the basic equation to calculate a -rough- number for maximum SPL output based on a driver's sensitivity and maximum rated power specs?

driver specs: _____WRMS max; _____dB sensitivity @1w/M; QTY____ speakers; = _____ dB max SPL at 1 meter


For example:

If I want to use qty=4 Acme model #1 speaker which the manufacturer says handles 100 WRMS, offers 95 db SPL @ 1W/M, what would the output SPL be at 1 meter for these if I provided 400W to the whole group of them wired together in series/parallel so that they offer the same impedance as a single one?

..Todd

[David_Web]

Pro-Audio Calculators. Calculator page

And another useful tool.
Piston Excursion calculator

[taj]

Thanks David. But, I was looking for the equation so I could calculate it myself. That website's source code uses Spanish variable names which makes it a bit hard to understand the actual equation.

..Todd

[David_Web]

You might find something here you could use.
Audio calculations in English - acoustics calculator convert audio formulas microphone formula sound recording studio free audio calculator recording studio acoustic audio engineering online education sound calcs energy calculations - sengpielaudio

[taj]

Wow, there's too much information on that website. Let me see if I have this correct for my example above.

4 speakers with 100db sensitivity each would result in 112db sensitivity combined given 1 W of power (2x the +6db doubling of sensitivity per coherent pair).

400 watts would provide 26db power gain over the initial 1W. (10 × log 400/1 = 26.1 dB)

This results in a total of 112 + 26 = 138db SPL at 1 meter.

That looks about right intuitively. Is it correct?

[edit: I said 95db in the first message then I used 100 here. Oh well, same calc applies. just different results.]

[edit#2] Running this through the calculator listed in the first link gives the same results, so I believe I have it correct.]

..Todd

[kevinkr]

Note that half of the +6dB sensitivity increase comes from the fact that most speaker designers think of amplifiers as perfect voltage sources, for two drivers in parallel the power is doubled because the load impedance is halved. You also get an additional +3dB (double) acoustical sensitivity due to acoustical coupling between the drivers.

If you are wiring the speakers in series parallel AND the effective load impedance is the same as for a single driver then you only get the acoustical sensitivity increase which is +3dB for each doubling in the number of drivers.

So in your case given both the 4 speaker set up and the single speaker set up have the same load impedance amplifier power does not change therefore you get +6dB acoustical gain in sensitivity.

You would theoretically get 132dBSpl @ 1M for a maximum input of 400W, note that there may also be room boundary reinforcement of >3dB at low frequencies depending to some extent on placement.

RANT: I've always thought factoring in the effect of twice the available power due to halving the load impedance as an increase in driver sensitivity along with the acoustical sensitivity increase due to two coherent acoustical sources coupling was kind of bogus - and note that it only applies in the world of solid state power amplifiers because simplistically tube amplifiers deliver the same output power regardless of load impedance because a different tap on the output transformer must be used to minimize distortion and maximize power output. /RANT

[taj]

I understood the acoustic output was always +6db for coherent pairs (half of that for incoherent signals). The speaker impedance impacts how I generate/provide that 400W to the 4 speakers (from an amplifier load perspective), but I didn't think it impacted the output SPL once I delivered that power. No doubt I am confused.

Also, I used a power calculation (10log) rather than a voltage (20log) calculation since that is a more intuitive value to me. I haven't seen an amplifier that amplifies pure voltage.

..Todd

[kevinkr]

Originally Posted by taj

I understood the acoustic output was always +6db for coherent pairs (half of that for incoherent signals).
<snip>
Also, I used a power calculation (10log) rather than a voltage (20log) calculation since that is a more intuitive value to me. I haven't seen an amplifier that amplifies pure voltage.

..Todd

Your understanding is only true if the device driving the coherent pair is a true voltage source and that is because the load impedance is halved - doubling the power delivered to the coherent pair, that is where half (3dB) of the 6dB comes from, the other half comes from the acoustical coupling between a coherent pair. If the power delivered to the coherent pair is the same power that was delivered to one driver then you get the sensitivity increase derived from a coherent pair acoustically coupling. Using constant power as the basis of comparison rather than voltage shows you what the actual gain in acoustical efficiency is.

Just because an amplifier can deliver power does not preclude its being categorized as a voltage source or amplifier. The ideal voltage source would deliver constant voltage into any load impedance connected to its output. Most voltage amplifiers approach an ideal voltage source only under narrowly defined conditions - i.e. from something approaching an open circuit to some minimum load impedance at which point the amplifier cannot safely deliver the current to the load required to maintain the required output voltage.

Using the power equation was the correct decision since it is power delivered to the voice coil that makes the noise you hear.

[catapult]

Most drivers are excursion limited rather than power limited. The max power spec is what it takes to melt the voice coil at high frequencies. But the driver will exceed Xmax at far lower power at low frequencies. Makes the 'simple' math more complicated.

[planet10]

Originally Posted by catapult

The max power spec

Is often undefined as far as it was taken, and is more or less meaningless for home hifi use.

dave