Knowledge / Ship systems

Underwater radiated noise: measuring pressure and interpreting decibels

Read hydrophone levels, bandwidth, background correction and source estimates without confusing different acoustic quantities.

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A ship-noise measurement is meaningful only when its acoustic quantity, reference, frequency range, averaging period and measurement geometry are known. A number followed by dB is incomplete. Underwater received sound pressure, a propagation-corrected source estimate and biological sound exposure describe different things, even when their numerical levels look similar.

A hydrophone measures fluctuating pressure

Acoustic pressure is the changing component around the local static pressure. Its root-mean-square value, p_rms, is the square root of the time average of squared acoustic pressure over the declared interval. An RMS value is not a peak value. Very short high-amplitude events can have a modest long-duration RMS while retaining large peaks.

NPL’s sound-pressure explanation distinguishes pressure from intensity and identifies the underwater reference pressure as 1 μPa. Intensity is energy flow per unit area; deriving it from pressure requires assumptions about the sound field and medium. A hydrophone does not directly measure acoustic power emitted by the whole ship.

The reference is part of the result

Sound pressure level is L_p = 20 log₁₀[p_rms/(1 μPa)] in dB re 1 μPa. For p_rms = 1.00 Pa, the pressure ratio is 10⁶ and L_p = 120.00 dB re 1 μPa. Doubling pressure to 2.00 Pa produces 126.02 dB, not 240 dB. The increase is 20 log₁₀2 = 6.02 dB.

For the same medium and compatible field assumptions, doubling mean-square pressure gives about 3.01 dB. A pressure-level change does not by itself establish perceived loudness for a person or animal. Air commonly uses a different pressure reference, 20 μPa; subtracting the reference difference still does not make water and air biologically equivalent.

Convert voltage through the entire measurement chain

Hydrophone sensitivity relates output voltage to pressure. Its frequency-dependent calibration, preamplifier gain, recorder scaling and filters all enter the conversion. NPL’s sensitivity explanation describes both linear sensitivity and the conventional dB re 1 V/μPa representation. A negative sensitivity level is normal; it does not mean negative acoustic pressure.

Take a hypothetical flat sensitivity of 100 μV/Pa over the selected band. An RMS output of 200 μV before any additional gain corresponds to 2.00 Pa and therefore 126.02 dB re 1 μPa. If an unnoticed voltage gain of ten were included, the inferred pressure would be ten times too high and its level 20 dB too high.

A spectrum density is not a band level

A narrowband spectrum can separate shaft-related tones; fractional-octave bands can summarize broader frequency regions. Pressure spectral density has units Pa²/Hz, whereas integrated mean-square pressure has units Pa². NPL’s spectral guide explains why spectrum levels and sound-pressure levels cannot be compared without bandwidth.

For an illustrative flat density of 0.010 Pa²/Hz across a 100 Hz-wide band, integrated mean-square pressure is 1.00 Pa², giving 120.00 dB re 1 μPa. The density level is instead 100.00 dB re 1 μPa²/Hz. The 20 dB numerical difference comes from integration across 100 Hz, not a change in the source.

Subtract background energy, not decibels

Suppose a run gives 120.0 dB re 1 μPa and a representative background record gives 114.0 dB in the same band and averaging framework. Assuming uncorrelated, stationary contributions, the source-related level is 10 log₁₀(10^(120/10) − 10^(114/10)) = 118.74 dB re 1 μPa. Subtracting 114 from 120 would give a meaningless source level of 6 dB.

As total and background levels approach each other, this subtraction becomes sensitive to small errors and environmental change. It cannot rescue a run contaminated by an unrelated ship or strong deployment noise. The applicable measurement method determines whether correction or rejection is justified; this numerical example does not establish an acceptance margin.

Received level and source level answer different questions

Received level describes the sound at the hydrophone. A source estimate compensates for propagation under an identified model. NPL’s source-level discussion warns that treating a large nearby source as a point source can fail. An equivalent level referenced to 1 m does not imply a hydrophone was placed 1 m from the hull.

For an ideal point source in an unbounded, lossless medium, spherical spreading gives a distance correction of 20 log₁₀(r/1 m). At 500 m, that is 53.98 dB. Adding it to a hypothetical received level of 120.00 dB gives 173.98 dB re 1 μPa·m. This is an idealised source estimate, not a valid shortcut for shallow-water trials.

Standardized quantities keep the model visible

Surface reflection, seabed interaction, sound-speed structure, water depth and source aspect influence ship measurements. The public ISO 17208-2 abstract describes an equivalent monopole source level derived from deep-water measurements for broadside aspect at a specified nominal source depth. That scope matters when comparing published numbers.

Radiated noise level and equivalent monopole source level should retain their proper names. A conversion defined for one geometry cannot simply be copied into a harbour. The public abstract identifies the standard’s scope; it does not provide enough information to reproduce its full procedure or claim conformity.

Repeat the operating condition as well as the track

Useful records include shaft speed, vessel speed, draught, machinery combination, propeller condition, hydrophone depth, closest approach and timing. Calibration must cover the relevant frequencies. NPL’s 2014 good-practice guide addresses system calibration and separates ambient sound from equipment and deployment self-noise.

If a later pass is quieter but occurs at another load or background condition, the cause remains ambiguous. Repeatable geometry and matched operation help distinguish an intervention from normal variation. Reporting uncertainty and individual run spread is more informative than retaining only the lowest recorded number.

A quieter measurement is a bounded finding

Two independent equal contributions of 120 dB sum to 123.01 dB, so removing one gives only a 3.01 dB reduction. This energy arithmetic helps explain why improving one machine may produce a limited whole-ship change. Coherent tones require phase-aware treatment rather than this simple independent-source sum.

IMO’s ship-noise overview places measurement within broader noise-reduction management. A reduction in one band, aspect and operating condition should be reported at that scope. Ecological interpretation additionally needs exposure duration, location, species and an appropriate assessment framework; a single broadband number is not a universal biological safety limit.

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