Amp Watts & Speaker Sensitivity

[Gabriel]

This really confuses me. I've been doing a lot of research lately as I've been looking at new amplifiers, and one of the things I've been worried about it wattage. However I've been reading on various forums and websites that increase in watts doesn't necessarily mean and increase in volume and that actually speaker efficiency plays a big part.

Apararently with every increase of 3dB we hear a doubling of volume, but how does this apply to speaker efficiency? At the moment I use a 50 watt amplifier with a 98dB sensitivity speaker, how would this compare with a 22 watt amp with a 103dB sensitivity speaker? Would the power/efficiency be similar?

I probably should have paid more attention in gcse physics...

[Pens]

http://www.300guitars.com/articles/ampl ... -decibels/

There is also the issue of speaker efficiency to consider as well. The efficiency of a speaker which is also called “sensitivity� is a measure of the speaker’s output (in decibels) with a specific amount of amplifier power (watts). Most often this is calculated by placing a microphone that is connected to a sound level meter at a distance of one meter away from the speaker. One watt of power is then sent to the speaker while the sound level meter measures the loudness in decibels. The output level results in a measure of efficiency. Another way to look at it is how efficiently does the speaker use the power. For example a speaker rated at 90dB will take twice the amplifier power to be the same volume as another speaker rated at 93 dB efficiency just like in our Marshall 50 watt vs 100 watt example. By the same token a speaker rated at 93dB will need ten times more power than a speaker with a 103 dB efficiency rating to be at the same volume. So you can now see how a relatively low powered amp with highly efficient speakers can be louder than a higher powered amp with much less efficient speakers. I’ve actually seen this situation a few times over the years

[Pens]

At the moment I use a 50 watt amplifier with a 98dB sensitivity speaker, how would this compare with a 22 watt amp with a 103dB sensitivity speaker?

So, to do the maths (if I follow the article I linked right), the difference in the two speakers is 5. This means to push the first speaker to the same level you'd need an amp that's 5 times as powerful.

50/22 = 2.27, ie the 50w is a little over twice the power of the 22w. To make the 22w sound as loud as the 50w with 98dB, you'd need to pair speakers with just around 100dB sensitivity.

So, for your example, the 22w with 103dB speaker would be almost twice as loud (really? that doesn't seem right...) according to 3dB resulting in doubling of perceived loudness.

The other way to put it, to make the first speaker sound as loud as the 22w/103dB you'd need a 110w/98dB amp setup.

I think that's what this means. I have no idea how true it is.

[Gabriel]

Cheers man, so basically the 22 watt amp should in theory be louder?

[Pens]

If coupled to that rating of a speaker, the math says it ought to be.

I cannot personally attest to any of this, I'm just going by what I'm reading here and doing the math. I've not actually ever tested any of this. And besides that, I play through a Fender Twin Reverb which gets louder than I can ever fathom using for shows at my level, even at 85w, so I have never bothered chasing anything louder.

[Pens]

Man, I did too much digging into this one.

So, according to a surprisingly normal post on Yahoo, the formula is

10*log(amplifier power in watts) + speaker_efficiency

http://answers.yahoo.com/question/index ... 120AA4vPLz

For the 22w/103dB combo: 30.91 (rounding to 31) : 31 + 103 = 134dB

For the 50w/98dB combo: 39.12 : 39 + 98 = 137dB

So, actually no. I think the article I linked oversimplified the equations.

Note, those levels are at 1m from the speaker, and diminish quickly the further out from the speaker, at a rate of 6dB per doubling of distance.

However, it's only a difference of 3dB between the two, though that's enough for the 50w to sound like twice as loud as the 22w.

This sounds a lot more "right" to me than the other one, so I trust the above equations more than the article.

Wolfram Alpha link if anyone wants to doublecheck my maths. Just replace the 50 with 22 to get the other result.
http://www.wolframalpha.com/input/?i=10+*+log%2850%29

[Pens]

FICK MICH.


Okay, so more searching around brought me to this nutty gonzo site with a bunch of maths all over the fucking place, at the bottom is a calculator for what we are trying to determine here.

http://www.sengpielaudio.com/calculator-efficiency.htm

Now, this one is giving me results similar to what my desktop calculator gave me and shows the 22w/103 combo as being slightly louder by about 2dB than the 50w/98 combo.

It's up to you to determine who to trust. I have no effin clue anymore as to which equation is correct.

[honeyiscool]

I'm pretty sure that the 22w/103 will be louder than the 50w/98 combo. However, here's the other thing.

103 sounds like the kind of numbers Eminence would give, and 98 looks like the kind of numbers Celestion gives. Celestion's 100 dB is a lot louder than Eminence's 100 dB from my experience.

[Bacchus]

A five decibel difference in speakers would make one almost four times as loud, no?

+3 is doubled, then +2 is almost doubled?

[NickS]

If my memory serves, .4771 is log 3, so 5 dB is just over 3 times louder.


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