Underwater Acoustics

The source level concept is strictly applicable only where the sound energy flows steadily away from a source with no reflection or scattering, as shown in the Concepts home page animation. However, it has proved to be a useful means of characterising sources in more general conditions.

A simple source is even more idealised, being omnidirectional, and emitting sound at one frequency. Its power (W) flows outward to be uniformly distributed over an area 4πr² of an imaginary sphere of radius r. This is called "spherical spreading". The intensity I, or power flux, is then related to the power W and the sound pressure P at this radius by:

where ρ is the fluid density and c is the sound speed in the fluid. This shows that:

which is a constant if W is stable and the fluid properties do not change.

Although originally devised for tank measurements of small sources at short ranges, source levels have been used at larger ranges and for larger sources such as ships. By making measurements at different ranges, the range over which the constancy of the P·r product is adequate is found. It then becomes a valid measure of the output of the source within this range. Its SI units are Pascal·metres.

So the sound pressure P, when measured at a known range r, is a measure of the performance of this source. The source output S, in this direction, is the pressure range product P·r. This is closely linked to the "source strength", measured as the rate of change of volume, or "volume velocity". However, the source output S is a more practical measurement, given the availability of accurate hydrophones.

The source level SL is then the decibel version of the source output S, just as the sound pressure level PL is the decibel version of the sound pressure P (see SI units).

When the sound is reflected, so that the power flux is no longer flowing away from the source, the simple relationship breaks down. In test tanks, measurements can be made quickly before the reflections invalidate the spreading law. When this is not possible, an alternative measurement of the total power can be made by using the properties of a reverberant tank. Reverberation also becomes important at longer ranges in open water, as the direct path sound levels decrease. In contrast, if the source is too close, or too large, it no longer approximates to the idealised point source, and the relationship again becomes inaccurate.

The decibel source level SL is given by SL = 20 log (P·r). Because the value of SL is equal to the sound pressure level SPL at a unitary distance, the reference unit is often given as "μPa at 1m". However, "μPa·m" is more concise, and does not suggest that the measurement must be made at 1m range. For many larger sources such as a ship at sea, the source level concept has adequate validity over a wide range, but is invalid when too close, when it becomes inappropriate to consider it as a point source.

When the source is known to be omnidirectional, the total power is determined by the source level provided the fluid specific acoustic impedance ρ·c is known. For typical seawater where ρ is 1030 kg/m³, and c = 1500m/s, the source level for a 1 Watt output is SL = 170.9 dB re 1 μPa·m.

The corresponding source output is 351 Pa·m.