Underwater Acoustics

The decibel scale is a logarithmic means of presentation, rather than a unit. Where there is considerable variation in magnitude it forms an alternative to the scientific notation, also used to present such values in a compact form.

As an example, the standard reference sound pressure in water is 1 μPa (microPascal). This can be presented in alternative formats:

1 μPa

0.000001 Pascals

1x10^–6 Pascals

0 dB re 1μPa

All these have the same meaning, and the presentation chosen is best determined by the anticipated use. Logarithmic scales, used for slide rules since 1620, were developed to assist scientists and engineers to make design calculations, particularly where multiplication and division dominated the work.

The decibel originated with the definition of a "bel", the logarithm to the base 10 of the physical value. By convention, this is applied to physical parameters based on power measurements, such as the Watt and the acoustic intensity I, in W/m². However, a logarithm can, strictly, only be taken on a unitless ratio.

Decibel scales are used to measure absolute values as well as ratios, but in this case it is vital that the reference level is specified. For example, the intensity level (IL) is the logarithm of the ratio of two acoustic intensities, but one (I_o) is a standard reference level, such as 1 watt/m²:

The intensity is related to the sound pressure P by the specific acoustic impedance "ρ·c" of the fluid in which the sound waves are propagated:

where ρ is the fluid density and c the speed of sound. So the sound pressure level is given by:

Where the energy is related to the square of a parameter, it is the ratio of the squares which is required. This changes the multiplier from 10 to 20. Voltage measurements can be given as a decibel voltage level "VL", where:

The presentation has been made easier by the use of the "dBV" convention, rather than "dB re 1V", making it clear that the reference is 1 volt. In air, a similar condensed form, the "dBA" has been adopted, with an implicit specification of reference level of 20 μPa, as well as a carefully defined spectral distribution. In underwater acoustics, the spectral distribution needs to be independently specified, and the reference level is usually 1 μPa.