Monthly Archives: September 2013

Of Watts and Volume

There is an equation for watts to decibels, given a sensitivity of x decibels, (1w/1m)!  Wattage must double for each increase of 3db.  See here and here for more info.  So that sensitivity (SPL) score is a pretty crucial starting point for a speaker.  Not that adding more amplifier watts is not impossible, just moderately costly.  But then again, in the case of an amplified PA speaker with 700 watts peak (and 350 RMS) then you’ve a lot of power.  By my calculations, taking a 98db SPL woofer up north of 122db, and a 110db SPL tweeter up past 134db – past the threshold of pain!  Also, I’ve read that perceptively, humans believe +10db makes one sound twice as loud as another.

BUT distance from the speaker matters!  On a ratio of 1/d^2, the sound gets softer the further away you are!  If pumping 350 watts through that woofer gets us 122db, standing 52 feet away from it, it will sound just like it we only pumped in 1 watt at 1 meter = 98db.  That’s still plenty loud.

It makes sense to me now why stage monitors are always like 100-150 watts.  Even with all the noise on stage, you’re pretty close which means they’re pretty loud.

Here’s what that speaker system sounds like as the watts are increased:

Watts Woofer Tweeter
1 98 110
2 101 113
4 104 116
8 107 119
16 110 122
32 113 125
64 116 128
128 119 131
256 122 134
512 125 137
1024 128 140
2048 131 143


Contrast that with another system with a higher SPL:

Meters Woofer Tweeter
1 122 134
2 116 128
4 110 122
8 104 116
16 98 110
32 92 104


For reference, here is a reference table for decibels:

Source Intensity Level (db)
Threshold of Hearing (TOH) 0
Rustling Leaves 10
Whisper 20
 Quiet bedroom at night 30
 Quiet library 40
 Average home 50
Normal Conversation 60
Busy Street Traffic 70
Vacuum Cleaner 70
Busy road 80
 Diesel truck, 10 m away 90
Large Orchestra 98
Walkman at Maximum Level 100
Front Rows of Rock Concert 110
 Chainsaw, 1 m distance 110
 Threshold of discomfort 120
 Threshold of pain 130
Jet aircraft, 50 m away 140
Instant Perforation of Eardrum 160

How Geography Dictates Fates

I just watched a documentary on Netflix that was based on Jared Diamond’s book, Guns, Germs, and Steel: The Fates of Human Societies and I’ve been moved. Jared lays out the major factors for why some societies are wealthy and others are in poverty, and they all boil down to one thing: geography. It’s not this simple, but the idea is that temperate climates, combined with high-yield crops like wheat which allow for farm animal domestication, allow people to spend time developing new technologies to fulfill and build wealth. Where these things have not existed, we find poverty and the conquered.

Well worth my time to watch, and I’ve added the book to my list to learn more. It’s quite sad, but also encouraging.