Something may surprise you about the following phrases: I have a 45 dB hearing loss, a 45 dB noise exposure is not considered harmful, this machine has a 45 dB noise level. The “45 dB” does not stand for the same sound level in each of the statements. Although few non-scientists know the technical definition of the decibel, the common understanding of the term is not seriously misleading.
dB is an Unit-less Logarithmic Ratio.
The decibel, strictly speaking, is not a unit of energy, power, or a sound level. The Merrium-Webster Dictionary defines a decibel as “a unit for expressing the ratio of two amounts of electric or acoustic signal power equal to 10 times the common logarithm of this ratio.”
So the decibel is a ratio, much like a percentage. What is the meaning of the following sentence? Last month, I lost 10% on my diet? Well, the meaning depends upon answering the question, 10% of what. If the sentence means 10% of my previous 150 pound body weight, then I would have lost 15 pounds. If the sentence means 10% of the 5 pounds I gained on my vacation, then I would have lost just half a pound. So the actual amount lost depends upon the reference value from which the percentage is calculated.
Like percentage, the decibel is a ratio. To calculate decibels: 1) First, divide the measured energy or power by the reference value. 2) Then, take the logarithm (to the base 10) of that quotient. 3) Multiply the result by 10 (for ratios of two powers) or 20 (for ratios of voltage or current). Simple? Right?
As a very arbitrary example, let's use 1800 watts as our base reference, because 1800 watts is the limit for many typical household circuits. (1800 watts = 15 amps X 120 volts). To express the power of a 100 watt light bulb in decibels (referenced to the 15 amp household current), the following calculation should be made:
10 log (100 / 1800) = -13 dB
Notice that the decibel value is negative, meaning that the value is below our reference; the power used by a light bulb is within the specifications of the circuit. In our example, a significantly positive dB level would blow a fuse.
Decibels on a Volt Meter
Meters on audio electronic equipment are often marked in decibels. The use of the decibel unit may lead one to mistakenly assume that sound is being measured, but the decibel refers to a ratio of voltages. It is often written as dBV for clarity.
dB SPL (Sound Pressure Level)
When dB is used to refer to sound intensity without a reference being given, the author usually means dB SPL. SPL is an abbreviation for Sound Pressure Level which is 20 micropascals. This level is two ten-billionths of the atmospheric pressure. There is an assumption that the ideal, young, undamaged ear can hear a sound at this level if the sound's pitch is at the individual's most sensitive frequency. In reality, few individuals can hear 0 dB SPL. The value of 20 micropascals was chosen so that all decibel values would be positive.
Audiometry and Hearing Loss
On an audiogram, 0 dB represents the hearing sensitivity of an healthy adult. The sound pressure level for 0 dB, as expressed in micropascals, varies at different frequencies on an audiometer. Individuals are most sensitive to sounds between 2,000 and 4,000 Hz. More physical sound energy will be represented by 0 dB at 500 Hz than at 4,000 Hz.
Notice that on an audiogram, a hearing loss is plotted below the 0 dB line but is marked with a positive dB integer. Better than normal hearing is plotted above the 0 db line but denoted with a negative dB integer. It all makes sense, because an individual with better than average sensitivity will require less sound to hear a tone.
dBA / dB(A) and Noise Level Meters
Noise meters generally use a filter, called the A Scale, which reduces the contribution of frequencies either below 800 Hz or above 10,000 Hz. The filter approximates the inverse of experimentally determined equal-loudness curves. The higher the value on an A-weighted noise meter, the more annoying the noise will be perceived. Levels below 85 dBA are felt to be safe under most conditions.
Noise above 10,000 Hz is not adequately measure by a noise level meters. Consequently, hearing loss might occur when intense high-frequency noise is present, even if that noise registers a safe level on a noise meter.
Conclusion
The decibel (dB) is a unit-less, logarithmic ratio that is used to designate the power or energy of sound and electric currents. The exact meaning of the dB is known from the context in which it is used. Most individuals have a adequate working knowledge of the decibel, even if they do not know its precise definition.
Sources and Other Notes
- The definition of a decibel as a unit-less, logarithmic ratio is known throughout the fields of acoustics, engineering, physics, audiometry, and otolaryngology. A highly technical article on the decibel, with all the formulas, is available on-line from the Physics Department of the University of New South Wales.
- Decibel: a unit for expressing the ratio of two amounts of electric or acoustic signal power equal to 10 times the common logarithm of this ratio from Merriam-Webster Dictionary on-line.
- Hertz: a unit of frequency equal to one cycle per second from Merriam-Webster Dictionary on-line.
- Pascal: a unit of pressure in the meter-kilogram-second system from Merriam-Webster Dictionary on-line.
Richard Walloch - Don't believe me because of my education or professional experience. Believe me because of the evidence and arguments I advance.
