Wattage and Loudness: Subwoofer

Audio has so very much more to it than expecting to hear the same 'loudness' from two different speakers powered from the same source, that I can't even begin to explain...

Maybe the speaker's efficiency, enclosure, resonant frequency, complex impedance, the location, the room acoustics, the type of magnet, the coil.....

Then we come on to more interesting problems such as the damping offered by the amplifier driving the speakers and so on...

Oh and not forgetting the response and physiological expectations of the human ear and brain interpreting the output...

A very complex situation - John.

Check the Theil/Small parameters for each speaker. One of these rates the driver for efficiency. It is expressed in db/m/watt or something like that.

The TS parameters describe the driver's response to a number of things like excursion, piston area, efficiency, frequency response, transient response, and dampening among a few. These parameters allow you to design an enclosure that allows the speaker to perform at its designed ratings.

The other reason they sound different is probably due to the fact that the enclosure probably is not optimum, so there are different levels of system efficiency in play.

Speaker wattage only tells you how much power the motor of the driver can handle without damage, but nothing about how well it works or sounds.

As already mentioned, there is a lot more to speakers, or drivers as we called them, than just wattage. There are generalities though. A 150W diver is usually (emphasis on the usually) smaller in size than a 400W driver. What this translates to is that the larger driver moves more air than the smaller one.

There's also the resonant frequency for the driver. Your test frequency may be equal to the resonant frequency of one of the drivers.

As already mentioned, wattage only tells you how much power the driver can handle, not how well it can convert electrical signals to sound. I don't know how it's done now, but back when I worked on sound systems, the decibel (dB) figure gives you an idea of how loud the driver is.

Thanks for the replys, those things are good to know.

It's so very easy to over simplify what is a very complex and also subjective science. I'm going to attempt to try and answer your query in a few sentences. I can't score 10/10 for this, I know....

To get an idea of what the effect of power may be (GIVEN that all things are equal, which is seldom the case as has been illustrated above), you can use the formula;

db = 10 X common log of P1 over P2

6 db would give an approximate doubling in actual / perceived output.

Thus we would require a drive of 400 W to provide about double the power from 100 W. In theory...

For many years it has been common practice to drive multiple drive units to provide a "larger/louder" sound stage. It's all down to how efficiently we can shovel air. As a common cone loudspeaker nears the extent of it's travel, the resistance increases enormously, thus it's far more efficient to drive larger cones or multiple units at below their rated drive capacity.

For the purpose of illustration we will assume that a 300 mm diameter loudspeaker driven 5 mm will displace 353 cm3 of air, using 50 Watts of drive.

The driver has a capability to travel 10 mm, but this requires a drive of 400 Watts to reach this cone excursion due to the increased resistance to movement.

Therefore to shovel double the amont of air would require 8 X the power (or about 1.5 X louder using our formula above).

If we drive two loudspeakers with a drive of 100 Watts, we would theoretically displace double the amount of air with only double the power.

Power equals work done, we can't get around this, but if we eliminate part of the work to be done (a lot of the resistance), we can certainly put the power to more efficient use.

My illustrative numbers may not be all that accurate, but I hope you get the idea.

The learned gentlemen who have commented previously are absolutely correct, there are an awful lot of different parameters that also contribute to the overall effect.

As a generalisation, bigger is best. A large loudpeaker in a large enclosure will produce better results, but the matching of the enclosure to the spaekers characteristics and the quality of the driver are also of great significance.

Loudspeaker (driver) design and enclosure matching becomes more difficult & critical as we reduce the size of the enclosure relative to the driver.

I'm waxing verbose, my apologies.

Peter

"6 db would give an approximate doubling in actual / perceived output.

Thus we would require a drive of 400 W to provide about double the power from 100 W. In theory..."

Errrm I think you have confused things a bit, the human ear has a logarithmic response (roughly), so 6 dB increase is a doubling of power applied to the speaker but it certainly isn't a doubling in *perceived* output or loudness by the ear...

Take an output of 60dB if you doubled the power into the speaker by increasing this to 66 dB the ear would only just detect this as a 10% increase in 'loudness'...

As to your statement that you would have to increase the power from 100 Watts to 400 Watts to provide double the power, this is plainly misleading, doubling the power from 100 Watts is to input 200 Watts, its quadrupling the power that gives 400Watts...

I think you're confusing power input to the speakers with power output from them and with perceived loudness...

In fact I'm now confused... John!

Let's not over-complicate things. The situation is:

• two drivers, one is 100W and the other is 400W. There is no mention of size or sensitivity.
• input a single frequency into both drivers at 100W.

The belief is that the 400W driver will seem to be louder. Is this psychological or physiological?

A driver's sensitivity is measured in dB at 1 meter distance from the driver with 1 watt input. This information is not given. It's the one piece of data that will tell us how loud a driver can be at 100W. Without it, we can only speculate.

The power of a loudspeaker depends on how is physically made its voice-coil. The higher the power, the larger (and heavier) the coil. The heavier the coil, the lower its natural frequency of oscillation (resonant frequency). This is the mechanical aspect.

Now, the electrical aspect: you have to check the electrical impedances of the two subwoofers. Could also be an impedance mismatch!

The best way to understand what is the difference between the two loudspeakers is to inject a pure tone from a signal generator (Sine) into the amplifier and to measure the voltage on the load with an oscilloscope (or use a PC-scope + generator and skip the amplifier). Varying the frequency (sweep between 0-100Hz) you can actually find the resonant frequency of each loudspeaker. When reaching the resonance, you'll notice a maximum of the voltage (rms) and the current is consequently the lowest - meaning that the voicecoil is working at its best efficiency. Mechanically, at resonance, the excursion is maximum.

Graphing the response of each subwoofer will show that they have different resonant frequencies - i.e. at a given tone they work with different efficiencies!

Todays loudspeakers are typically very inefficient at converting electrical power to sound power and there may be big differences depending on the quality of design and construction. This is probably because it is cheaper to build more powerfull amplifiers than better speakers. Another reason may be size. To be efficient you must match the impedance of the driver to the driven medium, air. The best way to do this is with an exponentially expanding horn like you see on many wind instruments. For base tones this horn should be 15-20 feet long which won't fit in many livingrooms. My dad had a Klipsch Horn which is a folded up approximation of an ideal horn. He drove it with a 1 Watt amplifier and I'll bet it produced more sound power with 1 W than your subwoofer can with 100W. I can tell you it rattled the windows.

hello frnd

here we clearly know that a woofer of high range have more complxity compared to that if the lower one but according to the device eqipped in the subwoofer the frequency het changed and automaticlly if a freq of 100 is applied the devuce with larger woofing capacity will rock as per the eqippment

What is the Impedence of the Subwoofer???, a Sub with an Impedence of 4 ohms will "sound" louder then a Sub with an 8 Ohm impedence under the same input conditions.

Watts are watts, but only if you're dealing with all other varaibles the same. I also agree that the enclosure will have a great impact on the "punch" that the sub exhibits. With a sealed enclosure, the punch will be tighter, but will exhibit a little more residual resonance, where as a vented enclosre will punch and stop.....a lot less resonance...

Something troubling me is the statement that 6 dB implies doubling of power. WRONG!!

If you are measuring power... db = 10 log (P₁/P₂).

If you are doubling power, db = 10 log (2)... = 10 x 0.3010... = 3.010 dB

NOW if you are measuring voltage (or current) the equation becomes

dB = 20 log (E₁/E₂)

If you are doubling voltage, db = 20 log (2)... = 20 x 0.3010... = 6.020 dB

This is all due to the power equations P = I²R or P=E²/R.

It is the "E squared" (or I squared) that does it.

NOTE! All that dB implies is the relationship between two powers (in watts for example), or two voltages or two currents.

To measure the power going into a speaker, I would use an rms voltmeter to measure the voltage across the speaker. If the speaker is 4 ohms (for example), I would use

P = E²/R... = E²/4 and you can get the power into the speaker in watts.

On the acoustic end of things, I am totally out of my league, but I will guess that someone has a standard which I will guess to be dBs or dB sound in which they define 0 dBs to be so much sound. If you double power into the speaker, you might expect dBs to go up accordinely.

Anyhow enough of my educated guessing.

Bill