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Technical Question: SPL, decibel, Speaker Sensitvitites


Stephen328

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Ok, Im kindof baffled by this one and maybe someone can set me strait. First of all as I understand it, the decibel scale is logarithmic, and doubles in volume every 10 db. At least in human preception. Also I understand that when comparing loudspeaker sensitivites, or maximum acoustical output that the scale doubles in volume every 3 decibels. For example, a loudspeaker with a sensitivity of 98 db is twice as loud as one with a sensitivity of 95 db. Now by definition sensitivity is the SPL output measured at one meter from the loudspeaker powered by one watt. Henceforth, shouldn't a 100db sensitivity loudspeaker be twice as loud as a 90 db sensitivity loudpeaker? (at 1 watt). Whats with this 3db business? Is that an average of all posiible other wattages or something? Im kindof confussed. I may have overstated the question, maybe trevor can simlify it for me. Feel free man. I have a tendacy to over complicate things. Thanks.

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ok steph, here goes.

The efficiency of loudspeakers is measured in dB, or decibels, and loudspeakers on the market vary in efficiency between about 80dB and 100dB depending on the model. The problem is that for every 3dB you add to the efficiency of the loudspeaker is equivalent to doubling your amplifier power. Let me stress that again - adding 3dB to the loudspeaker sensitivity has the same effect as doubling your amplifier power. To give some examples:

example number one!

Imagine you have a set of factory-fit loudspeakers in your car, and you replace them with a new set with a better sensitivity. Say the old speakers had 80dB sensitivity and the new ones had 100dB. With the new speakers in, the stereo will be more than eight times louder, equivalent to replacing your 20 Watt RMS head unit with a 2,000 Watt RMS monster amplifier - which would destroy your speakers anyway! Of course a really loud stereo doesn't necessarily sound good, but imagine being able to turn the bass up so the sound is full and punchy, above all of the engine and road noise.

example number 2!

Your friend Ricardo has a two channel 100 Watt RMS amplifier in his boot, feeding two 250 Watt RMS 6x9" speakers in the rear deck, each with 85dB efficiency (he forgot that loudspeaker power handling doesn't affect the volume and bought high power speakers with low efficiency like the guy in the car stereo shop recommended to him). You, however, have a 25 Watt RMS head unit and have four 40 Watt RMS 6x9" loudspeakers, two front and two rear, with 93dB efficiency . Your stereo will have an extra 6dB SPL, that's twice as loud, and since Ricardo has probably spent twice as much cash as you and gone to a lot of trouble fitting that extra amplifier, he will look one quarter as cool.

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the only thing I don't like about people making claims like that is that a 20 watt amp and a 2000 watt amp will sound no where close to the same at 20 watts. the 20 watt would be distorting, the 2000 would be just getting started. but at any rate, thanks for the info.

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I think Steve (the questioner) and John (the answer) just said the same two things. They are though, the same two different things. One is the power, the second is how we hear power.

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One (the first) is the log function of electrical input, sound pressure output, and voltage sensitivy of the speaker. These all relate as stated.

To be technical, voltage sensitivity of the speaker and effecency are often a bit confused. In short, 2.828 volts RMS will produce one watt into a speaker, if the speaker has a resistance of 8 ohms. Then you get some sound pressure level measured at 1 meter.

A real speaker is not going to have an 8 ohm resistance over its range of operation. None the less we find it easier to use a constant voltage level and assume electrical power is being absorbed by an 8 ohm resistor.

Recall the formula for power is P=V*V/R. So if R = 8, you need V= square root of 8 = 2.828 to make P = 1 watt. That is why we see a voltage of 2.828 being used to measure voltage sensitivity. People go one step futher and say that voltage is considered inputing a watt, which is only true if the R is really 8 ohms.

Okay, perhaps too technical. Necessary for accuracy, before someone comes along and womps me.

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It is also correct that doubling electrical power (increasing voltage by a factor of 1.414) will lead to an SPL increase of 3 dB on your RS meter. Note that 1.414 is the square root of 2. Power in the equation doubles.

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So the next issue (the second one) is whether a 3 dB increase on the RS meter "sounds" twice as loud (doubling of electrical input, but what does it sound like to our ear). As metioned by both the questioner and the answerer, that is not the case.

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Rather, it turns out that a 10 db increase of SPL, and its twin, electrical power, by a factor of 10 , is necessary to make the music sound twice as loud. This is a bit subjective. You should try it for yourself with an RS meter.

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It is interesting to note that the decibel is 1/10 of a Bell. That "Bell" is named for Alexander Graham Bell". He was an audiologist before inventing the telephone. While the math is grounded in logarithms, the units of measure of Bell correspond to doubling of perceived level of loudness. It works out that one dB is the smallest change of level which can be perceived.

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There is some vindication of the manufactures of big amps. You really do have to go from 10 watts to 100 watts for the output of the speaker to sound twice as loud. But that will be with an inefficent speaker where 10 watts may not be enough to begin with.

Gil

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