decibel

To get a feel on decibels, a chart of various sounds and their loudness. And realize that for every 10 decibel increase you're increasing the volume of the sound by 10 times. 20 decibels, 100 times. It's a logarithmic unit.

rustling leaves: 20 dB
whispers: 30 dB
quiet home: 40 dB
quiet street: 50 dB
conversation: 60-70 dB
telephone dial tone: 80 dB
car in traffic: 85 dB
possible hearing damage over a long time: 90-95 dB
average Walkman settings: 94 dB
diesel truck: 100 dB
power saw: 110 dB
normal amplified music: 120 dB
point of pain and hearing damage: 125 dB
jet engine at 100 ft.: 135 dB
loudest rock music: 150 dB
loudest possible noise: 194 dB

The decibel (dB) is actually a ratio of two amounts power. It is commonly used to measure electrical power and the power in a sound.

If you have two power levels, say P₁ and P₂ then the ratio of these power levels can be expressed as:
R=10 * log₁₀(P₂ / P₁).

For example, you could say that a 60W light bulb uses 10dB more power than a 6W light bulb, and a 600W light bulb uses 20dB more power than the 6W bulb but it uses 10dB more than the 60W bulb.

In the cases where a decibel is used as an absolute unit (not as a ratio), one of the power levels (P₁) is an assumed reference. For example, the unit dBW means "decibels relative to one Watt." Thus you could say our 60W bulb uses 17.8dBW of power, and the 600W bulb uses 27.8dBW. dBm is another common unit which means "decibels relative to one milliWatt."

Back to decibels of sound. When people say a sound was a certain number of decibels they are implying dB SPL which means "decibels - sound pressure level." The reference for dB SPL is a sinusoid at 1000Hz which is just barely audible. Thus, 0 dB SPL is the threshold of human hearing. Therefore, saying rustling leaves correspond to 20dB SPL means that the sound of rustling leaves is 20dB, or 100 times, louder than the quietest sound a human can hear.

A great Japanese sake bar in NYC, with a lot of character. It is located in the East Village near Astor Place. To get in, you have to walk down a flight of stairs to a basement entrance and hit a buzzer. As far as I can tell, anyone who hits the buzzer gets let in during its hours (10 pm ~ 4 am). Still, it makes me feel 1337 buzzing myself in. Inside is a montage of Japanese artwork and sake memorabilia, roped off waiting area, and, if you're lucky, a cute smiling waitress with orange hair. Otherwise, you get a gruff frowning waiter.

Once seated, you find yourself in a dimly lit room, 'intimately' packed together. Elbow room is sparse, so I wouldn't goto Decibel with a group larger then 4. What gives Decibel its name is the loud music they blast; I have heard everything from Kraftwerk, Snoop Dog, Face to Face, Frank Sintra, and Japanese Pop that a gaijin like myself wouldn't recognize.

Beyond the eclectic music being played, the real reason to go to Decibel is the sake. They stock over 30 different types and are kind enough to categorize them into mild, dry, and very dry for the unknowing. Served either warm or chilled, they should have something for any sake lover. For those of different palates, they have a selection of mixed drinks (I've been told the litchi martinis are rawkin) and a small list of food (the edamame is yumm-o).

So if dim, loud, and good are adjectives for your kinda places, give Decibel a poke.

When Alexander Graham Bell (harbinger of telemarketers and your future brain tumor) invented the telephone, he needed a simple way to deal with the changes in power that occur from transformer to transformer. Hence the Bel, commonly expressed in decibels (dB), a logarithmic ratio of change between two signals. The decibel, as it turns out, can also be used as a handy dandy reference with numerous applications, especially in the fields of electronics and audio, and also plate tectonics.

The decibel, as the unit of acoustic pressure that it is most widely refered to, is a logarithmic ratio of pressure, also known as dB SPL (or Sound Pressure Level). An increase in 10 dB SPL is an increase of pressure by a factor of 3.16. Sound is pressure. However, the way we perceive sound, a difference of 10 dB SPL is only twice as loud, so a nearby jackhammer (140 dB SPL) is 64 times louder than a standard dial tone (80 dB SPL). The range of human hearing is commonly understood to be between 0 dB SPL (the threshold of hearing) and 120 dB SPL (the threshold of pain), though obviously we can hear sounds above 120 dB SPL (just not very comfortably or clearly). Negative sound pressure levels exist, but humans won't be able to hear them until 5242 AD.

Decibels are calculated thusly:

For power (in Watts), dB = 10 log₁₀ (P₂/P₁).
For voltage and pressure, dB = 20 log₁₀ (P₂/P₁).

So a doubling of power is 10 log₁₀ (2/1) = +3.01dB
and a halving of power is 10 log₁₀ (1/2) = -3.01dB
and a tenfold increase of power is 10 log₁₀ (10/1) = +10.00dB
and a change of power by one tenth is 10 log₁₀ (1/10) = -10.00dB
and you can also figure that 5 times power is roughly +7dB (because you're halving a tenfold increase, right?) and 1/5 is -7dB and so forth.

Decibel references are also important. Because saying something is operating at +4dB is effectively meaningless (as opposed to saying that a +4dB gain is present), it is useful to have a couple of constants to compare levels. A decibel reference is a way to understand the relationship of power or pressure levels.

Here is a list of common references, where the reference is substituted for the input in the decibel equation:
0 dBW = 1 watt
0 dBm = 1 milliwatt
0 dBV = 1 volt
0 dBu (or dBv) = 0.775 volts
0 dBµ = .000001 volts (1 microvolt)
0 dB SPL = .00002 pascals

Different references have different uses. A common one (dBu) is used to explain the voltage of electronics independent of the load. For example, professional audio equipment runs at a nominal operating level (0VU) of +4dBu, or 1.228v (20 log₁₀ 1.228v/0.775v = +4dBu) and consumer audio equipment runs at a level of -10dBu, or 0.245v (20 log₁₀ 0.245v/0.775v = -10dBu).

We could also tell that a microphone which has an overload limit of 130 dB SPL starts clipping when exposed to 63.24 pascals (and that 1 pascal is about 94dB SPL, which is also about where, according to OSHA, sustained exposure causes hearing loss).

When adding references (say 7dBV + 3dBV), each individual reference must first be extrapolated into its base unit (in this case, volts, so: 7dBV = 2.24v and 3dBV = 1.41v) and then added (3.65v) and then recalculated into the reference (20 log₁₀(3.65v/1v)=11.25dBV). They may not simply be added together.

Decibels are handy if you want to gauge what is happening in an audio system due to changes in the fader (or volume knob or any variable amplifier for that matter), or need to know how much power you're going to be sending through your system after a gain stage (or anywhere through any electrical system).