MISCELLANEOUS TECHNICAL ARTICLES BY Dr A R COLLINS

# Sound Pressure Levels

## Underwater sound pressure levels

Set out below is a table of sound pressure levels in order-of-magnitude steps. Sound sources typical of some of these levels are shown for comparison.

### Broadband versus narrow band measurements

The sound pressure levels in the table are broadband measurements, where all frequencies from a few Hz to a few kHz contribute. For narrow band signals such as sonar transmissions the broadband level will be the same as the spectral level at the transmission frequency since all the power in concentrated at this frequency, but for a broadband source like a large merchant ship, the typical spectral level will be about 160 dB re 1µPa/Hz and the total power received over a 10 kHz band will add 40 dB [10×log(10,000/1)] yielding a measured value of about 200 dB re 1µPa.

### Spherical spreading effect

Measurements are standardised to refer to the sound pressure level at a distance of 1 m from the source. A few values at other distances are provided in the table to demonstrate the effect of spherical spreading of the sound waves. Spreading loss is 6 dB for each doubling of the distance from the source, so a level of 200 dB at 1 m will have dropped to 194 dB at 2 m and to 158 dB at 128 m and so on.

Pressure
(Pa)
Pressure
(dB re 1µPa)
Underwater sounds
1,000,000 240 Maximum linear source level.
Cavitation begins to occur at the face of transmitters.
Seismic air gun (1m from source)
100,000 220 Typical active sonar transmission level
Beluga whale call (1m)
10,000 200 Large ship, broadband (1m)
1,000 180
100 160 Large ship, broadband (100m)
10 140 Fin whale call (100m)
1 120
0.1 100 Ambient noise, sea state 4
0.01 80
0.001 60 Ambient noise, sea state 0 (flat calm)
100µ 40
10µ 20
0

Table 1. Typical Sound Pressure Levels for various sources.

## Comparison of underwater and airborne sound

To make a comparison of these underwater sound pressure levels with the values quoted for sounds in air an important point must be addressed. The sound pressure levels in air are usually referenced to the threshold level for human hearing which is now standardised at 20 µPa. Thus if an rms sound pressure level of 100 Pa is measured in water the result is quoted as 160 dB re 1µPa, whereas the same level in air is quoted as 134 dB. The conversion factor of 26 dB [20×log(20/1)] is due to higher reference level, but mention of the different reference level is often omitted.

The comparison of Intensity values corresponding to the air and water measurement are also subject to a large adjustment before meaningful comparisons can be made.

The relation between pressure and intensity is often quoted as P2 proportional to I, but this is only true if the acoustic impedance is constant. Acoustic impedance is a measure of how the pressure in the medium rises when a sound of a given intensity is applied. If the impedance is low, say 415 Pa.s/m as in air, there is a small rise in pressure. If the acoustic impedance is high, say 1,540,000 Pa.s/m as in water, the rise in pressure is approx 3700 times the rise in air pressure for the same intensity wave.

So to compare a sound pressure level in air and water, take the sound pressure level of a loud rock band of say 120 dB re 20µPa and find the sound pressure that would be observed in water for a source emitting at the same intensity. There is an additional 26 dB because the measurement is from a reference level of 1µPa instead of 20µPa, and there is 36dB additional rise in pressure due to the higher impedance of water. So the value measured will be 180 dB re 1uPa. A noise level of 180 dB is the roughly the noise level heard from a large container ship about 10 m away.

Comparing the noise a conventional submarine whose sound level, at worst, would be little more than the background ocean noise, to a rock band indicates that someone may have misinterpreted the sound measurement scales.