How LOUD will it be?

From N-Track Wiki

When purchasing a PA or keyboard monitor, we need to know how loud it will be.

Frequently, people discuss the option of powered speakers and talk about how many watts they have. However, the Watts rating does not tell you how loud it will be!

Use Watts to compare amps when you already have speakers, and know the max power rating for the speakers.

Use Watts when you already have an amp, with a rated output, and are looking for speakers in the right power range. But you look at the speaker efficiency rating to see how loud they'll be.

Of course, volume isn't everything. But to figure the volume (and why else to care about watts?), you need to figure the SPL level.

The formula is:

 Max SPL = Efficiency + 10 * log(power)

where

 Max SPL is how LOUD it is, in dB SPL (SPL = sound pressure level).
 Efficiency is rated for the speaker, at one meter distance, fed a standard tone at 1W power level.
 log(x) is the logarithm (base 10) of the given value
 power is the amp's or speaker's max power level, in watts, for the given speaker load in ohms

An important fact that helps to keep in mind is that 10 more dB means "sounds twice as loud to the human ear". Really, this is the very definition of the dB.

An important consequence: It takes 10 times the watts to be twice as loud

So, when comparing two speakers, if one speaker has 10dB higher efficiency rating, it will take a tenth the amp power to get it as loud as the other.

Here are a few other helpful items:

 3 dB = twice as much power, noticeably louder
 6 dB = 4 times as much power, significantly louder
 6 dB = twice the amplitude
 9 dB = 8 times the power, nearly twice as loud
10 dB = 10 times the power, twice as loud

Using the items above, you can figure out loudness without using a calculator. Here's a real-world example, the GEM PXA250 "all-in-one" PA. It has a 15" speaker (should have good bass response), 250W into 8 ohms, and an 8-ohm speaker with an efficiency of 100 dB SPL.

100 dB SPL at 1 watt (according to specs -- speaker efficiency)
110 dB SPL at 10 watts (10 times the power adds 10 dB SPL)
120 dB SPL at 100 watts (ditto)
123 dB SPL at 200 watts (twice the power adds 3 dB)

What about the extra 50 watts? Forget 'em, they're hardly worth mentioning. (400 watts would be 3 more dB, so 50 would be about less than 1 dB, which most folks can't even detect.)

So, how loud is that? Here are some guidelines.

 60 dB SPL - living room conversation level
 90 dB SPL - typical stage level for a loudish acoustic act
100 dB SPL - typical stage level for rock band; low end.  Louder than it should be.
110 dB SPL - high end stage level for rock band.  Not a good idea.
120 dB SPL - you're damaging your ears!

Now, note that these are overall stage levels -- walking around with a meter, you'd get louder spots and quieter spots. On the other hand the speaker volume we calculated above is pointing directly at the speaker, dead center in front of it, and only 1 meter away. So, obviously you want higher levels for a stage monitor, and also considerably higher levels for stage mains. I won't talk about volume levels for audience in venues -- it varies widely and so many venues are way too loud.

IMHO, The 123 dB SPL GEM is loud enough for a keyboard stage monitor, and reasonable for a PA for small gigs -- except that having only one speaker is limiting in terms of placement. In other words, assuming it sounds good, it should make a good starter PA for a garage band (and should be way loud enough in the garage). It may not be loud enough for a band with real high stage levels, unless placed close to the player, or if two are used.

Another thing to consider is what you'll be pushing through the system. If it's for voice, guitar, or keyboards without much bass, then the numbers are a good guideline. However, that SPL rating is for a 1 kHz tone. As you go down in frequency, it uses lots more power, so if you're playing bass guitar, you may need considerably more watts to get the same SPL. (For bass, square inches of speaker cone are very significant. More speaker area, better bass response.)

Now, what happens if we add another identical speaker? First, we need to know the amp's rating into 4 ohms, because doubling the speakers (in parallel, the usual way) cuts the ohms in half. I'll add more here later.

Cheers, Learjeff