# A Meter for Your Ears – Part II

I decided to rework the dosimeter a bit. Only a scientist could love a dB readout on the total integrated exposure. (me!) I also wanted to add a more realistic assessment of sound impact, rather than simple-minded integration.

Here’s my new meter after listening for 50 minutes to Fethercut by Les Jumeaux.

The top bars have been restored to duty as an RMS dB(A) meter, at all times, with 3s ballistics.

The bottom is a linear readout showing the percent of allowable daily integrated exposure. And you can see that, aft of my Crescendo, I received about 11% of the daily dose on that album.

On its face, that would imply that I could listen to 9 more 50 minute sessions. That would cover a day, but that seems light, and here’s why.

The simple minded literature suggests a maximum daily dose of 85 dB(A) for 8 hours, followed by a recovery period of 10 hours at 70 dB(A) or less. But recovery doesn’t just start up when you stop listening. It must be a continual process.

I also know that physics would suggest an exponential envelope on both attack and decay. So, as a first cut, I know that after 5.3 e-folding periods we reach within 0.5% of a steady signal’s value. So to make the meter read 100% after 8 hours at 85 dB(A), I’ll use a time constant of

$tc = 5.3 / (8 * 3600 * F_{samp})$

And as a first cut, 10 hours resting at 70 dB(A), following 8 hours of 85 dB(A), sounds like pretty much the same time constant on decay as on attack. So we’ll just assume that for now.

This approach, using 5.3 e-foldings, is more in line with actual experience. What that means is that after only 1 e-folding time of an hour and a half, you reach close to 2/3 of your maximum daily dose. (who would want to listen to that level of noise for 1.5 hours?)

And I have measured the half life of loud exposure effects in the past. I found about 20 minutes for the half life. But I’m willing to concede that my memory may be foggy, and a more safe estimate is the longer value of 1 hour (which is what an e-folding time of 1.5 hours implies).

So my meter will sit there and integrate upwards like simple integration, until after an e-folding time, it will proceed more slowly. After 4.5 hours it will be above 90% of daily dose, and finally reach 100% after 8 hours at 85 dB(A) SPL.

Not to be puritanical, that also means that if I take a break for a while, my meter will gradually relax its exposure estimate, and I can resume. The closer I get to my daily limit, the longer a full recovery will take. But I can get back 2/3 of my initial exposure by waiting for an hour and a half.

Okay, so while writing this post, I have been listening to Mezzanine by Massive Attack, at full nominal -23 LUFS level. So my exposure reading has also climbed to 15%.

I’ll play with the new metering for a few days to see how well it behaves with respect to reality…

• DM

## Author: dbmcclain

Astrophysicist, spook, musician, Lisp aficionado, deaf guy