What Does a Decibel Actually Measure? A Ratio Rather Than an Amount

A decibel expresses the ratio between two quantities on a logarithmic scale, and it is not a unit of sound or of anything else by itself. Quoting a sound level therefore requires a reference, and the standard one is a pressure close to the quietest sound a healthy young ear can detect, so a figure quoted in decibels for sound is a comparison with that threshold. The logarithmic form is used because the range of pressures the ear handles spans a factor of about a million between the threshold and the point of pain, which is unwieldy expressed directly, and because perceived loudness relates to physical intensity in a roughly logarithmic way, so the scale corresponds loosely to what people hear.

The consequences of a logarithmic scale are counterintuitive and specific:

• •An increase of ten decibels is ten times the intensity and sounds roughly twice as loud
• •An increase of three decibels is double the intensity and is barely noticeable
• •Two identical sources together give three decibels more, not double the number
• •Ten identical sources give ten decibels more
• •Levels cannot be added or averaged arithmetically
• •Doubling the distance from a point source in the open reduces the level by six decibels

The ear is far less sensitive to low frequencies than to those in the middle of the range, so a measurement giving equal weight to all frequencies does not reflect what somebody hears. Measuring instruments therefore apply a frequency weighting that reduces the contribution of low and very high frequencies approximately as the ear does, which is the weighting indicated by the letter A appended to a quoted figure and which is what nearly all environmental and occupational measurements use. A different weighting is used for high levels and for assessing low-frequency noise, where the first one underestimates the problem. Quoting a figure without stating the weighting is therefore incomplete, and comparing figures obtained with different weightings is meaningless.

The unit has a specific origin in telephone engineering. Signals travelling along a line lose strength, and engineers needed a way of expressing that loss that added up conveniently along a route, which a ratio expressed logarithmically does since multiplying ratios becomes adding logarithms. The original unit was named after Alexander Graham Bell and proved inconveniently large, so the tenth of it came into use and is what everybody now quotes. That history explains why the unit is dimensionless and why it appears throughout electronics and optics as well as acoustics, always expressing a ratio against some stated reference, with different reference quantities indicated by letters appended to the unit in each field.

Hearing damage depends on both level and duration, and the relationship is quantified in occupational standards. Regulations typically specify a daily exposure limit expressed as a level averaged over eight hours, with the principle that halving the duration allows an increase of three decibels since that is a doubling of energy, so brief very loud exposure is equivalent to long moderate exposure. Damage is cumulative and permanent, since it destroys sensory cells that do not regenerate in mammals. Impulse noise can damage hearing instantly at high enough levels. Personal listening devices are capable of producing levels that would require protection in a workplace. And the early damage affects frequencies above the range of speech, so it is not noticed until it is substantial.

The unit expresses a ratio on a logarithmic scale against a reference close to the threshold of hearing, not a quantity of anything. Two identical sources give three decibels more rather than double the figure, and ten decibels more sounds roughly twice as loud. Quoted figures are frequency weighted to match the ear's sensitivity, and comparing differently weighted figures is meaningless.