So a friend of mine who’s a reference librarian (and has a gaming YouTube channel you should check out) recently got an interesting question: how loud would a million dogs barking be?

This is an interesting question because it gets at some interesting properties of how sound work, in particular the decibel scale.So, first off, we need to establish our baseline. The loudest recorded dog bark clocked in at 113.1 dB, and was produced by a golden retriever named Charlie. (Interestingly, the loudest recorded *human *scream was 129 dB, so it looks like Charlie’s got some training to do to catch up!) That’s louder than a chain saw, and loud enough to cause hearing damage if you heard it consonantly.

Now, let’s scale our problem down a bit and figure out how loud it would be if ten Charlies barked together. (I’m going to use copies of Charlie and assume they’ll bark in phase becuase it makes the math simpler.) One Charlie is 113 dB, so your first instinct may be to multiply that by ten and end up 1130 dB. Unfortunately, if you took this approach you’d be (if you’ll excuse the expression) barking up the wrong tree. Why? Because the dB scale is *logarithmic*. This means that a 1130 dB is absolutely ridiculously loud. For reference, under normal conditions the loudest possible sound (on Earth) is 194 dB. A sound of 1000 dB would be loud enough to create a black hole larger than the galaxy. We wouldn’t be able to get a bark that loud even if we covered every inch of earth with clones of champion barker Charlie.

Ok, so we know what one wrong approach is, but what’s the right one? Well, we have our base bark at 113 dB. If we want a bark that is one million times as powerful (assuming that we can get a million dogs to bark as one) then we need to take the base ten log of one million and multiply it by ten (that’s the *deci* part of *decibel*). (If you want more math try this site.) The base ten log of one million is six, so times ten that’s sixty decibels. But it’s sixty decibels louder than our original sound of 113dB, for a grand total of 173dB.

Now, to put this in perspective, that’s still pretty durn loud. That’s loud enough to cause hearing loss in our puppies and everyone in hearing distance. We’re talking about the loudness of a cannon, or a rocket launch from 100 meters away. So, yes, very loud, but not quite “destroying the galaxy” loud.

A final note: since the current world record for loudest barking group of dogs is a more modest 124 dB from group of just 76 dogs, if you could get a million dogs to bark in unison you’d definitely set a new world record! But, considering that you’d end up hurting the dogs’ hearing (and having to scoop all that poop) I’m afraid I really can’t recommend it.

how loud something is depends on how far away we are from it. We know that when Charlie barked 113 dBA (assuming A-weighted) that he was some known distance from the sound meter microphone. But we don’t know what that distance was. A typical set back distance for a test like this might be 1 meter or possibly 3′.

The problem is that if we were standing in the middle of 1 million barking dogs we would not be hearing all the dogs with equal loudness. We’d hear the first 10 dogs around us with equal loudness and that adds 10 dB for total of 123 dB. But the next row of dogs will be twice as far away and there will be twice as many dogs in that row, 20 dogs. So we have 113 – 20 Log 2 + + 10 Log 20 = 113 – 6 + 13 = 120 from that second row. The combined total is 113 + 120 = 124.7 dBA for the first two rows of dogs.

The third row might have 30 dogs and be 3 times further away so their level would be 113 – 20 Log 3 + 10 Log 30 = 113 – 9.5 + 14.8 = 118.3 and total now is 118.3 + 124.7 = 125.6 dBA.

Next row is 4 times further and has 40 dogs so it delivers 113 – 20 Log 4 + 10 Log 40 = 113 – 12 + 16 = 117 when added becomes 125.6 + 117 = 126.2. And this doesn’t include consideration for the time delay and the Haas effect on loudness due to delayed sounds.

The next row is 5 times further away and has 5 times more dots, 113 – 20 Log 5 + 10 Log 50 = 113 – 14 + 17 = 116 + 126.2 = 126.6. The 6th row delivers 113 – 20 Log 6 + 10 Log 60 = 113 – 15.5 + 17.8 = 115.3 dBA which gives a new total of 115.3 + 126.6 = 126.9 dBA, and this is only for the total of 10 + 20 + 30 + 40 + 50 + 60 = 150 dogs in 6 concentric rows.

Each row contributes something but less and less. I’m sure there is a nice formula that gives us the sum of this progression out to 1,000,000 dogs. But we can clearly see that by 150 dogs, we thought worst case we might have 113 + 10 Log 150 = 113 + 21.7 = 134.7 dBA when in physical reality of dogs sitting in concentric circles we can only have 126.9 dBA.

moral of the story is if we were in the middle of a sea of voices, we only hear the collective voices of the first say 15 rows around us and all the rest become essentially inaudible to us.

Arthur Noxon

Acoustic Engineer