Underwater Acoustics

Most of the measurements described in the linked pages are described for a single frequency for simplicity. However, noise is almost always comprised of a range of frequencies, and its measurement requires more care.

Wide band noise has acoustic energy distributed over many frequencies, and for many purposes an integral over the bandwidth is useful. In idealised cases such as that of white noise, the consequences of such an integration can be set out simply.

White noise is defined as having equal energy, when time averaged, in each 1 Hz band over the total bandwidth considered. Whilst this is a theoretical concept, such noise can be made electrically by a digital psuedo-random noise source (PRBS). This only requires a shift register with suitable feedback, driven by a digital clock. At frequencies much less than the clock rate, the waveform is found to have the properties of white noise. If fed to a suitable (ideally matched) transducer, acoustic white noise can be produced. Outputs from other sources, such as a cavitating pump can also approximate to white acoustic noise.

In this case, the acoustic intensity and sound pressure can be defined as spectrum levels, relating to the energy in each 1 Hz band. When given in decibels, as is common, the underwater pressure spectrum level PSL is given by:

dB re 1 μPa²/Hz

where P²/B is the mean square acoustic pressure in a 1 Hz band. This is typically derived from a plot of acoustic pressure against time, using a Fourier transform to convert it into a spectrum plotted against frequency. The fundamental units are Pa²/Hz, or Pa²·s.

An alternative route to a spectral distribution is to use an electronic filter system to separate the bands. In this case, for practical reasons, the band widths are proportional to the band centre frequencies. Octave filters cover a range over which the frequency doubles. One third octave filter bands are also commonly available. The band width must be clearly stated in any results and, again, the fundamental units are Pa²·s. Because other calculations are routinely made as pressures, PSL is often presented as:

dB re 1 μPa/√Hz

This is formally identical, although the physical meaning of a square root of a frequency is doubtful. This equivalence is analogous to the voltage spectral level given as dB re 1V²/Hz or dB re 1 V/√Hz, also identical. However, it is vital not to confuse single frequency sound pressure levels with pressure spectrum levels. They have different units and are not comparable. For example, single tone audiometry threshold levels are not comparable with noise PSL values, without considering the appropriate masking bandwidth.