In acoustics, unlike most other fields, measurements are usually presented in the logarithmic format of a decibel scale, often misunderstood. It is then important that the underlying physical parameters are also well defined by suitable SI (Systeme Internationale) units. These units are described here and in the linked pages to minimise the confusion which can arise when the physics is concealed within the decibel presentation. This includes the issue of adding decibel levels (click on underlined items for more details).
Sound pressure is the most easily measured quantity and provides the basis for the most commonly encountered decibel level, the audio band sound pressure level in dB(A), as used in airborne acoustics. Underwater, the principles are similar but the reference levels use a different convention.

The idealised simple source, shown here by a pulsating sphere, radiates sound in all directions, to be received by the smaller spherical hydrophone, as the "pressure versus time" display. This measures the acoustic pressure P at this point, as it fluctuates above (red) and below (blue) the mean value. P is shown here as the peak to peak value, although the rms (root mean square) value is often used to give an average over a period.
A source level characterises the properties of the source by measurements using a hydrophone at a known distance. All finite sources can be considered as point sources when at a sufficient distance  the "far field". The alternate "pressure versus range" display above shows the pressure P falling as the inverse range. This gives a constant source output P·r in a specified direction which can be converted to the source level in decibels. Note that this concept is only valid in the far field with no echoes (spherical spreading).
A major benefit of the consideration of units is the opportunity to make a dimensional analysis. Where there is doubt, this reduces the risk of error, but requires that the calculations are made using linear equations.
The sonar equations which use decibel levels, so convenient for system planning, need to be backed by a clear understanding of the underlying physics. For example, the underlying equations predict the sound pressure created by one or more sources, placed at known positions and at known orientations, and measured by a hydrophone placed at the point of interest (but see adding decibel levels).
The sound pressure is linked to the source output power by calculations which depend on the directionality, but also depend on the environmental geometry and scope for echoes or reverberation. The fundamental assumption of spherical spreading, in conditions with no significant reverberation, is often adequate as a first step, but realistic conditions may require more complex calculations, leading to other spreading rules.
The receive sensitivity and transmit response, are important to link the electrical voltages and currents in the instrumentation used to measure, or to create, the sounds and noise of interest.
Issues of frequency distribution become important for all but the simple cases of a single sinusoidal wave. More complex waveforms transmit power at more than one frequency to give a spectral distribution. This will need to be integrated to provide data for specific frequency bandwidths or total power output. Here, in particular, it is beneficial to work in linear units which are more easily added than the decibel scale levels in which data is more often given.
In many cases, it is important to calculate the signal to noise ratio, which is used to estimate the likelihood of signal detection, or whether one source is audible over the other background noises. The detailed text explains why this "ratio" actually has units of time for conditions with narrow band (tonal) signals in the presence of broadband noise.
If you wish to send any feedback or have queries on the content of these web pages, please email Dr Dick Hazelwood.
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