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# Interesting presentation: Loudness vs intensity

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#### Hero999

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I came across this when doing a Google search for something else. One thing that interested me about this is that calculating loudness isn't simple.

Some people here seem to think that you have to multiply the power by a factor of ten to double the loudness, you don't, it's much less than thay.

If I double the energy of a signal without
changing the spectrum, the loudness will
increase by a factor of about 1.21
If we double the energy of a sine wave (to use a
simple example), its loudness rises by
approximately 2^(1/3.5).
$2^{\frac{1}{3.5}} = 1.219$ which indicates the figure os 1.21 was rounded down, it should be 1.22.

Using the law of indices tells me that in order to double the loudness of a sine wave, you need to increase the intensity by a factor of 3.5 not 10.

This confirms the results I've got from doing an experiment with a speaker and signal generator, I thought the figure was more like 4 but 3.5 is certainly believable.

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• Loudness vs Intensity.pdf
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When I was with Sony I did a lot of tests on this point. It definately subjective. Noise such as motor sound at lower frequencies is more annoying, hence intense than Vivaldi, therefore apparent loadness is greater. Db is a reading of sound energy but covers a large spectrum. Intensity is scource dominated, shape scource and proximaty of scource.This leads to the problem you have but explains why there are different speakers and different drivers for sound bandwidths.

Look outside the square and square it.

Sound level meters, at least the good professional ones have weighting networks that adjust the sound pressure levels to correspond to what the human ear "hears".

There are usually three different weighting networks provided, used for different applications, A, B, and C.

The most commonly used is the A frequency weighting network, and sound pressure levels are then quoted as dBA. The human ear is highly non linear in both frequency response and amplitude, so it is very difficult to give precise defined figures, because they vary so much.

Back in the 30's Bell telephone Labs did a lot of pioneering work work on audio measurements.
Interestingly the Bell, and decibel are named after Bell labs.
Fletcher and Munson also published their work on loudness curves:

The "Loudness" Control

Just an interesting corrollay.

You don't seem to see it much anymore but, it used to be pretty common for even home audio gear to have a "Loudness" control rather than a volume control. It would actually put in a weighting functlion to correct for what amounted to the Fletcher-Munson Curves. My recollection is that it added bass boost at low volume levels (somebody correct me if I got that backward).

Just an interesting corrollay.

You don't seem to see it much anymore but, it used to be pretty common for even home audio gear to have a "Loudness" control rather than a volume control. It would actually put in a weighting functlion to correct for what amounted to the Fletcher-Munson Curves. My recollection is that it added bass boost at low volume levels (somebody correct me if I got that backward).

I remember those, and your recollection is pretty much how I remember those loudness controls. Many used a potentiometer with a fourth connection, a tapping part way along the resistance track. That was used in conjunction with a capacitor, so that the frequency response changed (along with the amplitude) as the potentiometer was adjusted. Yup, bass boost at low listening levels.

Voltage vs Power

Some people here seem to think that you have to multiply the power by a factor of ten to double the loudness, you don't, it's much less than thay.

I don't want to presume too much here about what you are thinking but, let me suggest that it may be the difference between the 6 dB vs 3 dB for halving or doubling, depending on whether you are speaking in terms of voltage or power. The 10 log vs 20 log thing in the equation.

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