How do "decibels" work (in an easily, layman's understandable way)?

Factual Questions
1

What I am really after here is an easy and understandable way to describe decibels to someone else without a lengthy description. I know decibels is a logarithmic scale but I am hard pressed to say what that means in real world terms.

If I am at a concert and the decibels are 100 what would it mean if it was (say) 80?

20% (1/5) less? 4x less? What is 4x less if expressed as a percentage? I know this might be nonsense (if not I lucked into a right answer) which is why I am asking.

Ideally, I’d like an answer that is easily digestible to anyone and not some science level answer (well…both would be cool).

2

You are asking about perception, which also depends on frequency and a host of other factors. The rule of thumb is 10 dB = “twice as loud”

so 80 dB is 1/4 as loud as 100 dB

Usually people give examples, e.g., a normal conversation might be at 60 dB

3

The reason decibels are logarithmic is practical in nature. They describe a certain sound pressure change, and that can range from a few micropascals to 100 pascals. The perception of that sound pressure is logarithmic, meaning the difference from 80 to 81 dB is “the same” as the difference from 100 to 101 - even though the latter is a 20 times higher absolute difference.

I also find it not very practical to talk about “twice as loud” - you might as well say “twice as warm”, and that’s just not a thing (unless you are talking Kelvin, not Fahrenheit or Celsius). I also always cringe a little at comparisons like “as loud as a starting jet engine” - at what distance, I ask? Sound becomes quieter over distance, so without a measure of distance that comparison is meaningless.

Do try to remember some rough values - a quiet room, leaves whispering, quiet conversation, a loud rock concert, a gun shot. That can give you a much better feeling than saying “twice as loud”.

Here’s a handy chart.

4

Decibels can be applied to anything. In the electrical world, decibels (dB) are used for power.

Let’s apply decibels to the power of an engine. But we first need to define a “baseline” power. It can be anything. Let’s make it 10 horsepower (10 HP).

Here is the horsepower to dB mapping for the power outputs of six engines:

10 HP → 0 dB
20 HP → 3 dB
100 HP → 10 dB
1,000 HP → 20 dB
2,000 HP → 23 dB
10,000 HP → 30 dB

Here are things to be noticed:

The mapping greatly compresses the numbers; for a range from 10 HP to 10,000 HP, the decibel range is 0 dB to 30 dB. And it’s a nonlinear mapping.

If you double the power output of an engine, e.g. 15 HP to 30 HP or from 44 HP to 88 HP, then the power has increased by 3 dB. (Actually, 3.0103 dB. But we usually round to 3 dB.)

If you increase the power output of an engine by a factor of 10, e.g. 15 HP to 150 HP or from 44 HP to 440 HP, then the power has increased by 10 dB.

Here’s the data from 1 HP to 20 HP:

1 HP → -10.00 dB
2 HP → -6.99 dB
3 HP → -5.23 dB
4 HP → -3.98 dB
5 HP → -3.01 dB
6 HP → -2.22 dB
7 HP → -1.55 dB
8 HP → -0.97 dB
9 HP → -0.46 dB
10 HP → 0.00 dB
11 HP → 0.41 dB
12 HP → 0.79 dB
13 HP → 1.14 dB
14 HP → 1.46 dB
15 HP → 1.76 dB
16 HP → 2.04 dB
17 HP → 2.30 dB
18 HP → 2.55 dB
19 HP → 2.79 dB
20 HP → 3.01 dB

Note that a negative power level in dB simply means the power is less than the baseline power.

The equation for converting horsepower to dB is simple:

engine power in dB = 10 * log (engine power / baseline engine power)

where “engine power” and “baseline engine power” are both in HP.

5

I find it helpful for people to visualize/hear the dB scale by using a digital display A/V receiver. Many receivers have a display that shows the attenuation level of the amplifier output. For example, when the display reads “-30.0 dB,” the output is 30 dB LESS than some point determined by the manufacturer. (Of course, the efficiency of the speakers also plays a big role.) If the display reads “-27.0 dB,” the output is 3.0 dB LOUDER than -30.0 dB.

If you fiddle around a bit, you can see that changes of less than 1.0 dB are pretty hard to hear when you’re playing music or voice. It’s easier with a continuous tone. To make most material noticeably louder, you usually have to increase the level by 2 or 3 dB. This will give you a rough idea of how you perceive CHANGES in sound levels.

To increase the actual sound level by 3.0 dB, the amplifier has to change the output power (watts) by a factor of 2. If the system you’re using outputs 10 watts to produce an actual sound pressure level of 50 dB (as measured somewhere in your room), it must output 20 watts to increase the sound pressure level to 53 dB.

Distance from the sound source also has a huge effect. Doubling the distance from the sound source (speaker) drops the sound level by about 6 dB. If you’re 5 feet from a speaker and hear 50 dB, you will hear about 44 dB when you move back to 10 feet. Of course, room acoustics also play a huge role since they reflect and contain sound waves.

Finally, humans are pretty bad at judging sound levels accurately. Try having someone change the sound level on the receiver a bit (say, 2 dB) while you’re out of the room for 10 minutes. Then go back in and try to decide if the sound level is HIGHER or LOWER than it was previously. It’s more difficult than you think, though the difference between 48 dB and 52 dB should be pretty apparent.

6

A bit off topic but aren’t Kelvin and Celsius the same scale? Just different in how they assign numbers?

7

No: Celsius is not an absolute temperature scale, so you cannot say 2°C is twice as much energy as 1°C, but yes: as in just add 273.15 to get the number of Kelvins (so warming something up by 1 degree means the same thing in the two scales)

If you want to get historical, the original C scale was based on the physical properties of water, and it also had hotter temperatures = lower number

8

That was my point exactly. You might somehow say that 300K is twice as „hot“ (=energy) as 150K, but from a human standpoint, that’s completely meaningless.

9

Another thing about dB is that it can be used in three ways:

  1. It can represent a change in a value.
  2. It can be used to compare two values.
  3. It can represent an absolute value.

Note that #1 and #2 are essentially the same thing.

Here is an example for #1: “The output power of an audio amplifier increased from 30 W to 60 W. Therefore, the power increased by 3 dB.”

Here is an example for #2: “The output power of amplifier A is 30 W, the output power of amplifier B is 300 W, and the output power for amplifier C is 3000 W. Therefore, the power of amplifier B is 10 dB higher than the power of amplifier A, and the power of amplifier C is 20 dB higher than the power of amplifier A.”

So for #3… yes, the dB scale can be used to represent an absolute value of power, but everyone must agree on what the “reference” or “baseline” power is. In the electrical world, 0.001 W (or 1 mW) is often used as the baseline. So if the output power of an amplifier is 10 W, it means it has an output power of 40 dBm. Note the “m” added to the unit… it signifies the baseline power is 1 mW.

10

Unless the human is applying the Ideal Gas Law, or something where absolute temperature is not meaningless…

11

I think that, in human practice, “twice as hot” or “twice as cold” means “twice as far away from a baseline temperature that’s considered optimally comfortable”. So for instance, if we take our baseline optimal temperature as 72 F, then 52 is twice as cold as 62, and 92 is twice as hot as 82.

12

Have you ever, to yourself or anyone, said it was “twice as hot” as last week? I would not even know how to start interpreting such a statement.

13

The analogy to temperature is a good way to illustrate the idea of a reference level. If you try to say that 10 C is twice as warm as 5 C converting to Fahrenheit makes it 50 F is somewhat warmer than 41 F.

Another analogy could be reservoir water levels. Lake Powel is at 3517 feet above sea level today. That is way down from full at 3700 feet. The reference of sea level makes the numbers a little strange.

14

Temperature has always been screwy. An absolute temperature scale (e.g. Kelvin or Rankine) is “best” according to physicists, but these scales kinda suck when “regular” people are using them for things like ambient temperature. Hence the reason we have the Fahrenheit and Celsius scales. Physicists will scoff (and rightly so) at the notion of a negative temperature, but they still seems to work O.K.

15

I am certain this has been covered on these forums a couple of times, but the notion of negative temperature does make sense for certain systems. This was proposed by physicists and has been experimentally verified.

16

Before we drift any further, does the OP have any other questions about decibels?

Oh, and others have mentioned that using decibels as an absolute measure (as it usually is for sound) requires some reference value. For sound, that’s typically 10^-12 W/m^2, which is about the quietest sound that human ears can hear.

17

No…I consider my question answered and thanks to all who chipped in. Carry on and have fun. Still some interesting discussion happening (I think).

18

So, dumb question here (I never understood much math or physics):

What does it mean to say that horsepower = decibel? (Or, for that matter, 1 W = 30 dB)?

I’m confused about the three uses of dB here:

  1. As a “volume” to the layperson
  2. As a ratio between two measurements of power (?)
  3. As a measurement of power itself (?)

What does it mean to say that a certain power output is also a certain volume…? Like wouldn’t a 100W bulb “sound pretty different” than a 100W vacuum cleaner, the same distance away? Is there some secret connection between heat and what we hear as sound waves…?

19

AI says it’s because decibels are always a ratio, but the abbreviation doesn’t always make that clear, and there’s sometimes a hidden reference value?

In the case of watts, that would be 1 dBm (vs the reference value of 1 milliwatt)?

In the case of sound, that would dB SPL (sound pressure level), relative to 20 micropascals?

Is that correct…? So you wouldn’t really say that a light bulb sounds the same as an engine at a given power, just that it uses X more power (the decibel ratio). Same with sound. It only works when comparing two measurements of the same unit, or one vs the default reference value?

20

For background, the name decibel tells you a bit.. Deci means one tenth. Bel is named for Alexander Graham Bell, aka the inventor of the telephone. The Bel is the base ten logarithm of a ratio of power. But 10 times yields a more digestible number, so we have ten times the base 10 logarithm.

As noted above - since this is a ratio you need to define a reference level. That reference becomes 0 decibels.

For sound that pressure is 20 μPa - 20 micro Pascals. This is usefully about the threshold of human hearing.

The chart linked up above gives some useful references. In addition, 120dB Spl is often considered the pain threshold. 150 dB is instantaneous major hearing damage (up to and including permanent total deafness).

And as noted, human perception of loudness is itself not linear, and an increase in 10dB Spl is often considered to be perceived as a rough perceived doubling in loudness.

And to note - we measure pressure levels so it gets slightly messy, since power is proportional to the pressure squared. So you need 20 times the logarithm of pressure ratio to the reference. Same happens when you measure voltage - power is proportional to voltage squared, and so it is 20 times log voltage ratio referenced to a base voltage.