Frequency Specific Sound Reduction And dB Levels?

I started with a DIY construction project pertaining to sound-proofing; but now I'm feeling overwhelmed by a lack of knowledge on the physics of sound.

I've learned that sound reduction techniques have different levels of effectiveness based on their frequency.

I've also purchased this sound meter to measure the dB level, and I've used some software based tools on my laptop to attempt a spectrum analysis (similar to this) .

What I'm trying to do is predict how effective my sound-proofing construction will be against an 80 dB 'door slam' given it's various frequencies/levels, before I commit to a full-sized construction.

For example: If a wall has the sound reduction characteristics given in the chart above (and everything else is completely isolated) and a door is slammed - I know that the door slam doesn't occur at a single frequency like a musical note or a generated beep would. It's all over the place. Would I somehow calculate the 'average' frequency of the door slam and plot that against the walls sound-reducing chart to determine what level of sound reduction I can expect? Or, would it be more correct to calculate the individual reduction at various frequency ranges and alter the spectrum analysis appropriately and somehow 'sum' them to calculate the remaining dB?

Maybe it's more straight-forward to just ask how my sound meter is working? When it measures an 80dB door slam, is that the summation of all the audible frequencies or something else? Looking at the spectrum analysis I've posted, assuming my sound meter registered 80dB during that sound - If I could magically block all sound above 63hz and recreate the sound, how loud would the meter read? Would it still be 80 dB and only have a lower frequency. Or would the loss of the mid/upper frequencies result in a lower overall dB level (and if so, how could I estimate what it would be?)

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You assume the door slam is distributed across all audible frequencies equally, and just add up the reduction at all frequencies. The door slam is a sharp percussive event, and it will have Fourier components at all frequencies. – Ron Maimon Jun 23 '12 at 8:52

What Martin Beckett says is absolutely correct. However, the procedure for calculating the dB reduction of a particular type of wall insulation and a particular door slamming would be something like this:

1. Make a "dry" recording of the door slamming and put it on your laptop.
2. Do a spectral analysis on this signal. There will probably be a few frequency ranges that are much louder than others.
3. Take the "transmission loss" diagram for a type of wall insulation and convert it into a frequency response. That is, for each frequency, calculate $10^{-\frac{\text{power loss in dB}}{20}}$. This gives the amplitude of each frequency as a fraction of the original amplitude.
4. Multiply the two frequency responses together. (Multiply each frequency independently.) This is the spectrum of the sound you will hear when someone slams the door once the insulation is installed. Comparing it to the "clean" door slam (or, even better, to a recording of how it sounds with the existing wall) will show you how the insulation modifies the sound. This is useful information, because the bass and lower mid-range frequencies of a door slam are much more annoying than the treble ones, IMHO.
5. Calculate the power of the new spectrum and compare it to the old one.
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Thank you - very helpful – Rob P. Jun 23 '12 at 14:30

The total sound 'power' in dB is the measured result in each frequency band multiplied by a certain curve (https://en.wikipedia.org/wiki/A-weighting) - this takes into account that your ear is more sensitive to some frequencies.

If you take the sound meter app and slam a door you should see the power spectrum and you can see how well the proposed insulation would block each of the frequency bands

Unfortunately it then gets more complicated. Sudden short sharp sounds, like door slamming, are more annoying/noticable than more power but longer like rumbling traffic or thunder - so it's very difficult to say 'X' mm of insulation would reduce door slam by 'Y'dB and that is enough

ps. You might be better asking in the http://diy.stackexchange.com/ to see what other people fitted and how it helped

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ps. not really an expert on sound but hope this helps – Martin Beckett Jun 23 '12 at 4:25
Thank you - very helpful – Rob P. Jun 23 '12 at 14:31