Question re sound attenuation (caution: maths)

Forums › Off topic › Question re sound attenuation (caution: maths)

Jonski

265 posts

Ultimate Geek

#202051 15-Sep-2016 10:05

I'm confused. I used to be very good at maths (20 years ago) but my poor head... can anyone help me compare apples and oranges?

I'm looking to buy some double-glazed windows (IGUs). One manufacturer (let's call Brand A) claims an 80% reduction in transmitted sound from outside (down to 20%) for their IGU. Given a standard IGU (according to another manufacturer, Brand B) presents an inside volume of 48dB, what is the reference volume (in dB) Brand A refers to?

I'm assuming Brand A represents the standard IGU case. This of course may be open for debate.

Brand B says their IGUs have an inside volume of 35dB. What is the percentage reduction compared to Brand A's reference?

Extra info: Brand B also states that a 10 dB reduction is a 50% sound attenuation, that an open window is 80dB and a single-glazed window 60dB. This indicates a single-glazed window transmits 25% and attenuates 75% of the outside noise, being 2x 10dB reductions.

My first-approximation guess is that Brand A's reference volume is ~70dB (A half-open window?!?). The problem is that I'm aware logarithms can get away on you quickly. If anyone has had more coffee than me and is still attuned to their high school maths, feel free to wade in!

Cheers

Jon

I reject your reality and substitute my own!
- Adam Savage, Mythbuster

trig42

5787 posts

Uber Geek

ID Verified

#1630748 15-Sep-2016 10:23

Ouch, that makes my head hurt just reading it.

All I know is that the dB scale is logarithmic, so going upwards, a 10dB increase, doubles the 'volume' (SPL?), so I suppose it works backwards and your 75% would be about right. COuld be wrong - it has been over 20 years since I did any mathematics seriously...

Tradepub

Free professional, reference and technical white papers (affiliate link).

Fred99

13684 posts

Uber Geek

#1630784 15-Sep-2016 11:26

It's probably not even that simple. Presumably (double) glazing doesn't attenuate sound evenly across the frequency spectrum, so if for example a 10dB reduction was achieved at 1khz but only 3db at 100Hz, the birds might not wake you up in the morning but the rumble of traffic would anyway. If one used 1khz reference, and another used 500hz reference, then the results wouldn't be comparable.

Personally, I'd forget the maths unless you are trying to achieve a specific target as may be needed for an audiologist's consulting room etc. Thicker glass, laminated glass - including grades of laminated glass designed to reduce sound transmission probably have benefits in terms of increased thermal insulation properties as well.

Jonski

265 posts

Ultimate Geek

#1630835 15-Sep-2016 12:28

I think I've got it sussed... time and coffee have had their effect.

My mistake was trying to use log10, as that's what's in the online tutorials. However, knowing (now) that a 10dB increase is a doubling and that a doubling is 2^1, I figured that I take the overall dB increase (or decrease), divide by 10 and put that to the power of 2. I had been trying to divide by 2 and put to the power of 10 (or variations thereof).

So, 80 to 60dB is -20dB difference, or 2^-2, giving 0.25. That makes sense. Using this, I can calculate (taking log2) Brand A's reference volume is 71.2dB and that Brand B's product is a (100-8) or 92% volume reduction.

If anyone's still interested, changing the reference volume to that of an open window (80dB), Brand A transmits 11% and Brand B 4.4%.

Final comment: Brand A is classic aluminium joinery (with a thermal break) and Brand B is UPVC. I totally agree with Fred* that it's "not that simple" but it's also the best we have. I think I'll take the merits of these products to the DIY forum...

* And I studied Electronic Engineering at uni- I knew a lot about filters and response curves, and actually enjoyed Laplace transforms: take an equation, turn it 90 degrees to reality, manipulate it, turn it back 90 degrees, there's your answer!

Cheers

Jon

I reject your reality and substitute my own!
- Adam Savage, Mythbuster

frankv

5678 posts

Uber Geek

Lifetime subscriber

#1630883 15-Sep-2016 13:12

decibels is a logarithmic scale, so adding 10dB means multiplying the power (the loudness) of the sound by 10. However, hearing perception is also logarithmic... a chainsaw makes 10 times the sound power of a lawnmower (0.1W, 110dB vs 0.01W, 100dB) but a person wouldn't say it was 10 times as loud... they might say it was twice as loud. So 10dB is roughly a 50% change in perceived loudness.

I think that what Brand B is saying is that if you have an 80dB sound source (e.g. a loud alarm clock) outside an open window, it will sound about the same, whereas outside a single-glazed window it will sound like 60dB (hair dryer) and outside a double-glazed window it will sound like 35dB (a person talking).

An 80% reduction in sound power would be about a 2dB reduction (i.e. perceived about 10% quieter)... i.e. hard to detect. So that's probably not what they mean. Probably what they're trying to say is an 80% reduction in perceived loudness, which would be about 40dB (i.e. about the same as Brand B).

NB that it's all very well that the double-glazing attenuates sound this well, but a metal frame would be very good (compared to wood) at transmitting sound. And the walls around the window may or may not) be good sound insulation. So increasing the attenuation of the window area won't necessarily make for a large change in perceived sound levels.

And, I assume, these numbers will be averages across the audible spectrum, and there may be more or less attenuation at various frequencies.