|How much is 1000 dB?
by Jan Nielsen and my AMD XP 2000+ PC
It was a nice evening with the friends. Lots of music and red wine, just like it usually is when we gather around and enjoy our mutual hifi-interest. Many different kinds of music were thrown into the CD-player and at some time loud organ-music filled the room. It was one of the famous Dorian recordings. Immediately it caused some dissatisfaction with the speaker’s low frequency capabilities. "They lack weight and dynamics”, Peter said “Turn up the volume”. "Yes" John replied; "we got to play much louder – 1.000 dB!". The more technically minded among us looked at each other. 1.000 dB? Well yes, we could need a little more guts and punch in the low end, but that much? "Hey John, you don’t know how much 1.000 dB is", we remarked really better knowing. Then the subject was finished and we went back to the music and the red wine.
Well at home I thought about what we had said, and then asked my self “do you really know how much 1.000 dB is?". All this with dB is very incomprehensible and confusing for most of us, which may be caused by its basis in logarithmics. Before we try to make an example better to understand the 1.000 dB, we have to establish the fact, that this sound pressure is absolutely impossible. As sound is a variation in air pressure we can not come below zero. The highest sound pressure we know of must be a nuclear blast which is mainly artificially created very local high pressure (the blast) and therefore can reach around 200 dB. If we wanted to reach the 1.000 dB we would need power much larger than the largest nuclear bombs – in fact infinitely larger!
The problem is, that each time we want to create a 3 dB rise in sound pressure we need to double our power. Anybody remember the story about this very clever guy and the emperor of China? They played chess and the emperor promised him anything he would like if he won. He did win, but very modestly ask only for a little rice. “You put one corn of rice on the first square of the chessboard, 2 on the next, then 4 – 8 and so on until all 64 squares are filled” The emperor called for a sack of rice but soon found out that this wish were impossible to fulfil. The result would be more rice than we have in the entire world. In fact it would be enough to give each and every person on the planet 460 tons of rice! Where to put all this rice, the story does not tell.
In our little example with the 1.000 dB we have to double the power much more that 63 times and hence the numbers will be even more unimaginable. To do it a little more understandable I chose to start out with a fairly efficient speaker that will give 94 dB for 1 Watt. At the same time this fantastic speaker stands infinite power and it will be big – VERY BIG. In fact much bigger than possible. To reach the 1.000 dB we have to double the power 302 times. To make things a little more reasonable we say that we just need the 1.000 dB for one second – something like at single blast from the organ or a few beats on the drum.
After doing this little calculation (no problem for my PC) I got a very big number. But let us stop along the way. At approx. 1.000 W our speaker will give 124 dB, and to reach 145 dB we have too draw 100.000 W from our amp. At 1 MW (1.000.000W) our poor speaker will only give us 154 dB. To reach the 200 dB from the nuclear blast we have to put out 39.811.000.000 Watt. But there’s still a very long way to go. When we finally reach the 1.000 dB our gigantic super power amp must yield 3,9811E+90 Watt (=3,9811E+84 Mega Watt). This unfathomable and completely unimaginable big number has 91 digits – we have to be very close to the fantazillion!
To understand this little problem, we have to resolve the number into more imaginable bits (just like with the rice). As we can not eat power we got to transform it into something different – why not money?
Let us say, that our giant number is good old American Cents and that each living creature on the earth bigger than a fly were given an equal amount in 100 USD bills, then the height of each portion would be approx 1,1E+45 light years – in fact bigger than the distance from Earth to the farthest known star! That’s a lot of money.
No let us look at something more suitable for all this power. The worlds total use of power was in 1992 equal to 7.680.000.000 tons of oil. If we very optimistically say that 1 kg oil (2 lbs) equals 1.000.000 Watt and then double this amount to make the number look like the power here in 2002, then we will get 1,536E+12 MW. If we then divide this one year earthly power demand into our very big number, we get another very big number. In fact the power to create the 1.000 dB would be able to solve all power problems on the earth for 2,59E+78 years – an infinite amount of time, and again a number totally incomprehensible for our small brains..
We need something even more powerful so let us compare our power demand to the output of the sun. The sun radiates 360.000 trillion Megawatt (360.000.000.000.000.000.000.000 Watt) each second – not only light and heat but all kinds of radiation. If we take the above total earthly power demand for one year and divide this into 1 second of solar-power, we would get enough energy to supply our little green planet for more than 46.900.000 years (if we only we could!).
Our next little calculation is quite simple:
The speaker needs 3,98E+84MW
Each second the sun will give 3,60E+20MW
In other words our sun must burn for 1,11E+64 seconds to give the power we need for only one second. This means that the sun has to burn for 3,56E+53 years – a number with 54 digits – I do not know what to call it. The next problem is that our whimsy little sun will only burn for around 4.000.000.000 years – so long before we have reached the necessary power the sun has burnt out!
What we need is more stars like our sun. In fact we need the total power from 8,89E+43 stars equal to what our sun will put out in 4.000.000.000 years just to drive our speaker for one second!
Even though many stars are considerably larger than our sun and some may burn much longer, we can safely assume that our little speaker will need more power than the total amount of known stars will deliver in their whole lifespan – way into the future until all light is out and everything turns to dust and nothingness in the big ”gnab gib” (the opposite of big bang).
And then it’s not even stereo!
To make it all even more understandable (incomprehensible) our big number 3,9811E +90 is with a very big possibility bigger than the total amount of atoms in the known universe! And when even the number of stars and planets is close to infinity our number must be even bigger – my god the world of mathematics is wonderful!
Summing it all up, I would not like to experience the original organ recording at 1.000 dB, and I find it quite good that most of us can live with only 100 dB.
Finally a challenge. Who will calculate the voice coil temperature and XmaX of our speaker at 1.000 dB?