Here in Part 2 of our explanation of the dB, or decibel, we’ll continue to use money to demonstrate the why and how of it.  After today, you’ll have bragging rights in your home recording studio.

So far, we’ve been comparing dollar amounts. When we compare quantities, it can also be called a ratio. Comparing 1 billion to 1 million could be written as the number 1,000,000,000 divided by (or “over”) the number 1,000,000. Notice there are 9 zeros in 1 billion and there are 6 zeros in 1 million. If we actually divide 1 billion by 1 million we’ll get 1,000. How many zeros are in 1,000? You’re right. There are 3. Hmmm. All we had to do was subtract the number of zeros in a million from the number of zeros in a billion to get 3.

Scientists have used this knowledge to define a thing called a logarithm. Remember that from your high school math? Oh well, it won’t matter. In this case, all it means is, how many times do we have to multiply 10 by itself to get another number? In our case, it turns out to be the number of zeros in the number. (Please, don’t warp your brain trying to figure it out for a number like 5!) For now, all we care about are nice round numbers that are multiples of 10.

You can work this out for yourself, but if we multiply 10 by itself 9 times, we’ll get 1 billion. That means that the logarithm of 1 billion is 9. What’s the logarithm of 1 million? Right. It’s 6. What’s the difference between 1 billion and 1 million in terms of logarithms? Right again. It’s 3.

These numbers are known as logarithms to the base 10. Obviously, because it’s how many times you have to multiply 10 by itself to get the number. As you know, we use the decimal numbering system. It’s called that because it’s based on 10. You know, that’s how many fingers and toes you have. Scientists came up with the name decibel to refer to these ratios. The word has ‘deci’ which refers to the number 10, and it has ‘bel’ to honor Alexander Graham Bell. Thus, the decibel.

Okay. How does this relate to sound level and voltage? By now, you should realize that we’re comparing amounts of the same thing, or making ratios of the same things. In our case, we’ve been using dollars. In the case of sound, it is sound levels. Same for voltage.

One more definition.  The decibel is defined this way: the number of decibels is equal to 10 times the logarithm (to the base 10) of the ratio of the 2 quantities of things we’re comparing. Therefore, we can now say that 1 trillion dollars is 120dB compared to 1 dollar. That’s because the log (short for logarithm) of 10 is 1, and the log of 1 trillion is 12. The ratio would be 12 over 1, or 12. Then we multiply that by 10 and we get 120 dB.

Whew! Did you follow that? Anyway, remember our original challenge? How to show the difference between 1 dollar and 1 trillion dollars on a single piece of paper? If we now let 1 tenth of an inch represent 1dB, we only need 12 inches! Ok. Ok. That won’t fit on an 11 inch piece of paper. But it’s a whole lot closer than 100 billion inches.

You’ve probably picked up on the fact that 0dB and 120dB are terms you hear in the recording industry all the time when talking about sound levels. Now you know why the decibel is used to refer to sound levels. It’s a whole lot easier to talk about numbers like 0dB, 20dB, and 120dB than it is to talk about 1 micro something and 20 micro somethings, or 10,000 micro somethings.

You see, the sound levels that the human ear deals with go all the way from 1 microPascal (no way I’m defining that in this article!) to 1 trillion microPascals. You guessed it. That’s 120 dB. Just like the dollars.

Sound Levels Decreasing By 3dB Steps

Now you know what a decibel is, and why it’s used when comparing large differences in quantities, or amounts of things. It could be apples. The difference between a billion apples and 1 apple would be 90dB. Go outside now and breath some fresh air.

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One of the first terms you hear a lot when you begin recording music is “dee bee”. Everyone throws the term around and it’s in all the manuals that come with your music recording gear, but how many musicians really know what it means?

The ‘dee bee’ is written like this – dB – and is short for ‘decibel’. UhOh! Now we’re getting technical. Yes, it is a scientific term representing a concept that’s pretty difficult to explain – especially without using any math symbols and equations. Not to worry though, because I’m going to keep it simple.

When I was teaching recording engineering to high school students, I wanted to be able to explain the decibel in a fun and memorable way so that they’d really have a pretty good understanding of what it represented. That day in class became known as Mr. Likes’ famous “Decibel Lecture”.

In the recording industry, dB’s are most commonly referred to when talking about sound levels and signal levels, or volts. Before we get to those, I’m going to talk about money. Everyone can relate to money, right?

Here goes. For the sake of this explanation, we’re going to assume that the smallest increment of money is 1 dollar. When I was growing up, a very rich person was defined by 1 million dollars, and they were called “a millionaire”. I know, you’d consider yourself pretty rich if you had a million dollars. So would I. But, over the years a very rich person became defined as “a billionaire” – a person worth a billion dollars. What’s the difference between a millionaire and a billionaire? Well, it means the billionaire has a thousand times as much money!

Today, we hear on the news that the U.S. government is in debt to the tune of 14 trillion dollars!  How big is a trillion compared to a billion? Well, again, it’s a thousand times as big!

If I wanted to draw a line on a piece of paper going from the smallest increment – 1 dollar – to 1 trillion dollars, and I used a space of 1 tenth of an inch for each dollar, my line would have to be 100 billion inches long! believe me, that’s too long for an 11 inch long piece of paper.

Could there be a way for me to demonstrate the difference between 1 dollar and 1 trillion dollars and get it to fit on 1 piece of paper? AhHa! Here’s where the decibel enters the picture.

In Part 2, I’ll show you that it’s easy to understand the decibel without having to give you any math equations or goofy-looking symbols. Watch for it.

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