Underwater Acoustics

Sound pressure is the most easily measurable quantity. This is the fluctuation of the pressure in the fluid medium, usually air or water. Microphones measure the variation in air pressure, ignoring the steady atmospheric pressure, usually for audio frequencies 20Hz - 20kHz. Very slow variations at a frequency below 1 Hz are better considered as meteorology. Hydrophones measure the acoustic pressures in water, and are insensitive to the hydrostatic pressure, which is usually much greater than any fluctuation.

Although the SI unit of pressure is the Pascal, Pa (or N/m²), the standard reference pressure in air is 20 μPa (20 microPascal). Decibel sound pressure levels are the ratio of measured pressures to this value, expressed in logarithmic terms. The explanation for this apparently arbitrary level is that it is linked to human hearing and also to a more fundamental acoustic quantity, the intensity in watts/m². Whilst this power flux density is very useful for assessing physical effects such as localised heating, it is harder to measure directly and is usually calculated from the acoustic pressure and a knowledge of the fluid properties.

The specific acoustic impedance links the intensity to the sound pressure. This is the product of fluid density ρ (rho) and the speed of sound c in the fluid, usually written as ρc, although ρ·c is preferable. For a plane wave the intensity I is then related to the mean square pressure P² by:

For air at 1bar (100kPa) pressure and 20°C, ρ = 1.19 kg/m³ and c= 344m/s to give ρ·c = 409 kg/(m²s) or 409 Rayls, named after Lord Rayleigh. This value varies with environmental conditions at about 400–420 Rayls.

A reference level of 1 pW/m² for intensity was set in 1932 by the American Standards Association, and 20 μPa chosen for the reference pressure in air at the same time. Both are typical of the tonal threshold level of human hearing in its most sensitive frequency band 1 - 4 kHz. A 20 μPa acoustic pressure in air gives a 1 pW/m² intensity if the impedance is 400 Rayls. However, the same logic could not be applied to underwater sound, where the typical specific acoustic impedance value of 1.5 Megarayl for water would lead to a pressure standard of 1225 μPa. In 1970, the 1μPa pressure reference level was chosen by the US Navy for their underwater work.

Various derived reference levels include the hydrophone receive sensitivity level referred to 1 V/μPa. However, most hydrophone sensitivities are smaller than this by a factor of at least a billion, reducing decibel levels by >180 dB, and giving rise to the typical negative sensitivity decibel levels. The original aim of choosing the very small 1 μPa reference was to ensure that the pressure decibel levels were always positive, but this is ineffective here. Clarity is improved if linear hydrophone sensitivities in the more realistic units of μV/Pa are quoted, in addition to the decibel levels where required.