Speaker Sensitivity - a scientific approach

[Uk Ant]

Ok, so the sensitivity of a speaker is measured in db's per watt at one metre.
Guitar speakers seem to range from low 90's to just over 100.
So, what difference does this actually make (lets say that frequency response is pretty even).
Now, obviously if the actual wattage delivered to the speaker was the stated output on an amp we'd all be happy with 5w amps producing up to 500db or so.
For reasons involving the output transformers and some dull maths what is actually delivered to your speaker is much less than stated.
Now this is the thing, what is the typical wattage delivered to the speaker from your typical range of amps, say 5, 30, 50 and a hundred watts?

Can you then work out just how much volume you're really going to get from different densitivity speakers?

 

[SlyFoxx]

Re: Speaker Sensitivity - a scientific approach

Try this.

http://myhometheater.homestead.com/splcalculator.html

 

[marvar]

Re: Speaker Sensitivity - a scientific approach

A watt is a watt is a watt-
Most mfg rate their amps wattage at just before the power amp clipping begins.
The MV is not controlling the wattage output of your amp, only the sensitivity of it.
Now for the speaker part:
Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are actually very inefficient transducers; only about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to acoustic energy. The remainder is converted to heat, mostly in the voice coil and magnet assembly.

A speaker 3 dB more sensitive than another will produce double the sound pressure level (or be 3 dB louder) for the same power input; thus, a 100 W driver ("A") rated at 92 dB for 1 W @ 1 m sensitivity will put out twice as much acoustic power as a 200 W driver ("B") rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of input power. In this particular example, when driven at 100 W, speaker A will produce the same SPL, or loudness, that speaker B would produce with 200 W input. Thus, a 3 dB increase in sensitivity of the speaker means that it will need half the amplifier power to achieve a given SPL. This translates into a smaller, less complex power amplifier—and often, to reduced overall system cost.

 

[Uk Ant]

Re: Speaker Sensitivity - a scientific approach

Try this.

http://myhometheater.homestead.com/splcalculator.html

Cheers Sly, that's just the thing.

Using that funky little tool using a 30w amp at 3 feet (almost a meter) changing from a 97db/w to 100db/w will give you an increase of SPL (sound pressure level) from 112.5 to 115.5 db. Which is should be a noticable difference.

Bit of dodgy, not very scientific reverse math means our 30w amp is actually only delivering something just over 1w to the speaker.

 

[Fikealox]

Re: Speaker Sensitivity - a scientific approach

Now, obviously if the actual wattage delivered to the speaker was the stated output on an amp we'd all be happy with 5w amps producing up to 500db or so.

I think you're just a little confused on the maths. Basically, a 3dB increase is a doubling. For a 100dB speaker, 1W@1M = 100 dB SPL. For the same speaker, 2W won't give you 200 dB SPL, it'll give you 103dB SPL. [edit: I should add, a doubling of SPL won't equate to a doubling of subjective volume. IIRC, it takes about a 10dB increase to constitute doubled volume, which is why a 100W amp isn't anything like twice as loud as a 50W amp.]

As for actual wattage versus rated wattage... it varies from amp to amp and manufacturer to manufacturer. For instance, I have it on good authority that Marshalls of 100W and more tend to give more juice than rated, while Mesas tend to give somewhat less than rated.

 

[Rich_S]

Re: Speaker Sensitivity - a scientific approach

I don't know where you get this:

...5w amps producing up to 500db or so...

A 5 watt amp is going to give you pretty much that at the output. Doubling the wattage gives you 3dB. So, let's assume it's a 4-watt amp to make it easy.

A Celestion Greenback is rated 98 dB, 1W @1M. Double the power twice to get 4 watts and you add 3 dB twice, so you'll get 104 dB.

Consider an Eminence Red Fang... 103 dB, 1W @1M. So, the Red Fang will give you almost as much volume out of 1 watt as the Greenback gives out of 4 watts.

Imagine a little 12.5 watt amp with an ineffiecient 10" speaker - say, 97 dB. Retrofitting a Red Fang would be the equivalent of cranking that little amp's output up to 50 watts. This is why speaker efficiency is so important - it can make a small amp sound much more powerful, or tame a too-powerful amp.

Calculating a theoretical number of decibels from a particular rig is pointless - there are too many other factors involved: number of drivers, type, size, and shape of cabinet, positioning of the cabinet within the room, composition of the room surfaces. Even if you rrive at a number of dBs, it doesn't consider the EQ of the guitar sound, and whether it can cut through the band or not. It's easier to just use experience and rules of thumb to determine if an amp is loud enough for a certain application.

Speaker efficiency ratings are only useful for making comparisons among speakers.

 

[Uk Ant]

Re: Speaker Sensitivity - a scientific approach

A watt is a watt is a watt-
Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are actually very inefficient transducers; only about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to acoustic energy. The remainder is converted to heat, mostly in the voice coil and magnet assembly.
Most mfg rate their amps wattage at just before the power amp clipping begins.
The MV is not controlling the wattage output of your amp, only the sensitivity of it.
Now for the speaker part:
For example, a speaker 3 dB more sensitive than another will produce double the sound pressure level (or be 3 dB louder) for the same power input; thus, a 100 W driver ("A") rated at 92 dB for 1 W @ 1 m sensitivity will put out twice as much acoustic power as a 200 W driver ("B") rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of input power. In this particular example, when driven at 100 W, speaker A will produce the same SPL, or loudness, that speaker B would produce with 200 W input. Thus, a 3 dB increase in sensitivity of the speaker means that it will need half the amplifier power to achieve a given SPL. This translates into a smaller, less complex power amplifier—and often, to reduced overall system cost.

Now this is the bit where I get lost, the sensitivity is based on db/w now this is obviously not the wattage of the amps stated output, so is it the wattage after losses in the voice coil?

 

[Uk Ant]

Re: Speaker Sensitivity - a scientific approach

I think you're just a little confused on the maths. Basically, a 3dB increase is a doubling. For a 100dB speaker, 1W@1M = 100 dB SPL. For the same speaker, 2W won't give you 200 dB SPL, it'll give you 103dB SPL.

Ya know, once upon a time used to be much better at this stuff

Ok, so (and I hope this helps some other people), given a speaker of 100w efficiency, 1 watt gives you 100db, 2 will give you 103, 4 106... up say 120w giving you 121db.

Oddly my brain hurts less now.

I obviously need more of a refresher on maths.

 

[Rich_S]

Re: Speaker Sensitivity - a scientific approach

Now this is the bit where I get lost, the sensitivity is based on db/w now this is obviously not the wattage of the amps stated output, so is it the wattage after losses in the voice coil?

No.

"Watts" are watts delivered to the speaker terminals from the amp. All the watts go in, and they all get used up somehow.

Some get burned up in purely electrical heating. Some are wasted mechanically, overcoming the stiffness of the suspension, and constantly accelerating/decelerating the mass of the coil, cone, and suspension back and forth. All this energy is used up by the speaker, and radiated as heat. You're trying to separate the electrical losses from the mechanical, but nobody does that. It's a hair not worth splitting.

Whatever is not lost as heat, is transferred to the air and ends up as sound. That's what efficiency is: the amount of sound you get out for a given amount of power put in.

 

[GuitarStv]

Re: Speaker Sensitivity - a scientific approach

Don't forget frequency response. Our ears are not linear, and we don't hear things in a linear way. Upper mid frequencies are heard by the average person as being much louder than lower frequencies, so if you have two speakers . . . one with a 3 db boost at 100 Hz, and one with a 3 db boost at 2k Hz you're going to hear the second one as being much louder than the first . . . even if they're the same sensitivity level.

To further complicate things, we hear stuff differently at different VOLUME levels. When you're listening to stuff at quiet levels there is the appearance of hearing less bass, and at louder levels you tend to perceive more bass even if the bass signal has risen linearly with the rest of your output signal. Psychoacoustics is very messed up the more that you learn about it.

 

[Rich_S]

Re: Speaker Sensitivity - a scientific approach

Just more reasons while worrying about "the maths" and a scietific approach is pointless and a waste of time/brain cells (and this coming from an engineer).

We should all have spent this time practicing.

 

[marvar]

Re: Speaker Sensitivity - a scientific approach

Just more reasons while worrying about "the maths" and a scietific approach is pointless and a waste of time/brain cells (and this coming from an engineer).

We should all have spent this time practicing.

Well, yes, but we can't be practicing ALL the time! lol
It's a warm and fuzzy feeling ya' get when you can help explain things to others that you have learned over the years.
On another note- I prefer my Marshall with Greenbacks, although they are less effecient than an H30, orV30, I like the tone, I can turn the master volume up a bit more, for faster breakup w/o getting so loud.