Speaker cabinet properties

Incomplete, selective introduction by bassbacke (2004-01-21)

Constructive feedback is always welcome.

Efficiency

Maximum sound pressure may be calculated using the sensitivity information (dB SPL or dB@1 W@1 m) in combination with the maximum RMS power that can be applied to speakers. This is not entirely true since the closer you get to maximum rated power the less effective speakers are in producing sound rather than heat. Very few vendors give a maximum dB SPL value which really is how loud a speaker cab can be.

Human ears perceive a gain of +10 dB in sound pressure as twice the volume, a gain of +3 dB will be noticed.

In order to gain +3 dB in sound pressure, you need to double the amp power, but you need ten times the power to gain twice the volume (+10 dB) or a hundred times the power (ten times the voltage) to gain four times the volume (+20 dB). Then again human hearing will tolerate twice the volume only for 1/10 of the time, so be careful!

It takes only twice the power if you use twice as many speakers at the same power each to gain +6dB which is what you gain for carrying more. In other words twice the number of speakers at the same power add +3 dB. This rule can only be applied a very small number of times.

Let's compare two speakers and their "true max. volume":

Speaker A Speaker B
103 dB@1 W@1 m
300 W RMS
>max. dB SPL: 128 dB
98 dB@1 W@1 m
1000 W RMS
max. dB SPL: 128 dB

Let's conserve some energy here. :)

Please note that these figures are theoretical. Close to the maximum power load the coils in the speakers heat up and increase their electrical resistance hence they actually don't get driven at full power. Also often the maximum electrical cannot be applied since the mechanical limitations of speaker constructions. There is a limit how far a speaker membrane can move in or out and that limit may be reached far below the electrical limits. The above figures give an idea of how things work nevertheless.

Power vs. Sound Pressure

Power Sound Pressure
0.1 W -10 dB
0.2 W -7 dB
0.4 W -4 dB
1 W 0 dB
2 W +3 dB
4 W +6 dB
10 W +10 dB
20 W +13  dB
40 W +16 dB
100 W +20 dB
200 W +23 dB
400 W +26 dB
800 W +29 dB
1000 W +30 dB

Absolute Efficiency

Reading all these figures about efficiency you may have wondered what would be the absolute maximum sound pressure if all electrical power was converted into sound rather than heat. The answer can be found in the table below:

@ 1 W @ 1 m Efficiency
112 dB 100.00%
106 dB 25.00%
103 dB 12.50%
100 dB 6.20%
98 dB 4.00%
96 dB 2.50%
94 dB 1.60%
92 dB 1.00%
90 dB 0.60%
88 dB 0.40%
86 dB 0.25%
84 dB 0.16%
82 dB 0.10%
80 dB 0.06%
77 dB 0.03%

So, if anyone tries to sell you a speaker cab with more than 112 dB @ 1 W @ 1 m, you should not buy anything from this source. You can also see that 103 dB @ 1 W @ 1 m is already very good. Still only 1/8th of the electrical power coming from the amp actually is converted into sound and not into heat, so if your speaker cab can handle 800 W and you feed it that much, 100 W go into sound while 700 W of heat have to be cooled by the speakers internally. Not an easy task. However, a speaker cab like that is very likely to be very loud so make sure you don't harm your or anyone elses hearing.

Distance vs. Sound Pressure Loss

Each time the distance doubles 6 dB are "lost".

distance relative
loss
1 m 0 dB
2 m -6 dB
4 m -12 dB
8 m -18 dB
16 m -24 dB
32 m -30 dB

dB? How loud is that and how long can I stand it unharmed?

The numbers below are averages of noise per week a human ear can handle unharmed. Per week! It's not like we're all the same, not even same person handles noise the same all day every day, but it gives you a good idea of what's not good for you. ;)

sound pressure example duration/week
85 dB   40 hours
88 dB   20 hours
91 dB   10 hours
94 dB   5 hours
96 dB   3 hours
98 dB   2 hours
101 dB disco 1 hour
104 dB   30 minutes
107 dB   15 minutes
109 dB chainsaw 10 minutes
112 dB   5 minutes
114 dB   3 minutes
116 dB   2 minutes
119 dB   1 minutes
130 dB threshold of pain 6 second
140 dB 30 m from jet aircraft less than 1 second

If the noise levels and durations exceed what your ears can handle, use ear protection. They come in different shapes, colors, and frequency ranges. The maximum attenuation such a beast can give you is -30 dB which is mainly because there are other ways noise can reach you inner ears.

Compression?

A last word on the matter may be that compressed sound material will always sound louder than uncompressed material at the same power ratings so for you purists out there avoiding compressors, speaker cabs may never sound loud enough, I guess.  ;)

Impedance

Impedance is basically the (AC) electrical resistance of a speaker cab. It's measured in Ohm, which is the SI unit for electrical resistance. If you have more than one cab and want to connect your cabs to the same amplifier you can connect them in parallel or serial. Most people will connect them in parallel since it is far easier to connect that way.

Speakers Cabs connected in Parallel

If you connect speaker cabs in serial, just add the impedances. The German word "Reihe" in the picture below means "serial".

Speakers Cabs connected in Parallel

The general formula for calculating this for n speakers is:

1/Rtot = 1/R1 + ... + 1/Rn

If you connect exactly two cabinets in parallel the resulting resistance/impedance can be calculated like this:

Rtot = (R1 * R2) / (R1 + R2)

where R1 is the impedance of speaker cab 1, R2 is the impedance of speaker cab 2 and Rtot is the resulting impedance your power amp will have to be able to drive. This formula works no matter whether the impedances of the two given cabinets are the same or not. In any case if you add a speaker cab in parallel the resulting impedance is always lower than the lowest impedance of any single cabinet.

Example: R1 = 8 Ohm, R2 = 4 Ohm

Rtot = (8 Ohm * 4 Ohm) / (8 Ohm + 4 Ohm)
  32 Ohm² / 12 Ohm
  2,6 Ohm

However, if both cabinets have the same impedance, the formula can be further simplified.

R1 = R2 gives us

Rtot = (R1 * R1) / (R1 + R1)
R1² / (2 * R1)
R1 / 2

In other words two cabinets of the same impedance connected in parallel result in half the impedance of a single cabinet. Simple enough?

Example: R1 = 8 Ohm, R2 = 8 Ohm hence R1 = R2

Rtot = 8 Ohm / 2 = 4 Ohm

However, if you have two speakers in parallel with the same impedance the power coming out of the amp is divided into half for each speaker. That may still not be "bad" since most (transistor) amps deliver more power at a lower impedance. Just make sure you don't run your amps within the limitations designed by the amp manufacturer.

Impedance Matching

When it comes to power amplifiers there are basically two very different types: transistor and tube.

Tube Amps

Tube amps do not usually directly drive speakers. They use a transformer instead. To make a long story short, a tube amp won't be harmed (much) if the impedance of the speaker cab(s) connected is too low, but it won't work well or may even die on you if the impedance of the speaker cab(s) is too high. The worst you can do is to connect no speakers at all. Modern amps have additional circuits to prevent damage. Don't count on it. Some tube power amps can be switched/adjusted to different impedances. Make sure they match.

Transistor Amps

Transistor amps usually directly drive the speakers connected. To make a long story short, a transistor amp won't be harmed (much) if the impedance of the speaker cab(s) connected is too high, it will simply not reach the full power it can give when connected to the minimum impedance. However, if you connect too low an impedance to your amp it may die on you. The worst you can do is to short cut the power amp's output. Modern amps have additional circuits to prevent damage. Don't count on it.

Watts (Power Rating)

Watts (W) are the SI unit for power. When it comes to speaker cabinets it means the maximum power a speaker cabinet can handle. The power is produced by a power amp and driven into the speaker coils. The more power an amp drives into a speaker coil the more the speaker membrane moves air and hence produces sound. Unfortunately the wire in the speaker coil heats up a lot and even moving it and the speaker membrane will cool it only to a certain degree. Excessive heat gives us more than one problem. If it gets too hot, the wire can melt and the speaker dies. Also heat does not do much good to the speaker's magnets. Also the more heat, so the close you are to the maximum power you can run through a speaker, the less is the gain in volume.

Given all that one should not try to run speaker cabs all too close to their maximum power rating.

Power Matching

Amps should have more power than speakers can handle

Often people think their speakers should be capable of handling more power than the amp driving them. Their logic is that if the speakers can handle more, the amp can't hurt the speakers. Nice try. It's only working if you stay well below the maximum rated output of such an amp.

As soon as you drive an amp beyond it's maximum power rating, it goes into "clipping" which can end in nasty DC which will fry even the biggest speaker cab.

In short: small amps can easily kill even a speaker made for more power if driven too hard.

What about amps with more power than a speaker can handle? Simple. Don't drive them to their limits and they will bring your speaker cabs up to their full power with little or no risk. Even if you drive a speaker at a little more power than it's designed for it will handle it much more gracefully than any clipping amp.

So how much more power should one have? There are very different opinions out there. Some say add 50% of the speaker cab power rating, some aim for twice the power.

I have a pair of Flite 210H speaker cabs, which can handle 300 W each and have 8 Ohms each. In parallel they can handle 600 W having 4 Ohms. I don't have an amp that can produce 1200 W at 4 Ohms. I used to own a Sunn 1200S amp capable of 1200 W RMS output at 2 Ohms. The manufacturer Fender was unable to provide information as to how much power is available at 4 Ohms (I tried more than once by email) but I've been told from a reliable source it's about 800 W at 4 Ohms nd ca. 550 W at 8 Ohms. I took a number of precautions to keep my amp from clipping (compressor/limiter) and even pumping 800 W into such modern and highly efficient speaker cabs would be more like suicide than anything else. I used to like to have some reserve. These days I use a Markbass F-500 top at a max. output of 20-40 W. Ear plugs are no longer needed. Thanks to our drummer who play electronic drums.