# Sound Pressure Level

When we measure noise level we normally measure the sound pressure level and express the result as something like 85dB(A)

• dB is an abbreviation of decibel – the sound pressure scale is vast and so we take the logarithm of the measurement to make the numbers easier to handle
• A is an abbreviation for A-weighting – a simple filter that is applied to make the measurement more meaningful by by weighting the response to more closely match the human ear

below I’ve broken these expressions out into a bit more detail and have started to add some of the calculations to our workshop calculator that you can download as an excel workbook.

Sound Pressure Level or SPL – ten times the logarithm of the ratio of the time-mean-square pressure of a sound, in a stated frequency band or with a stated frequency weighting, to the square of the reference sound pressure of 20×10-6Pa.

Decibel – a description of the decibel is a good starting place:

The human ear responds logarithmically and it is convenient to deal in logarithmic units in audio systems. The bel is the logarithm of the ratio of two powers, and the decibel is one tenth of a bel.

The Bel was the amount a signal dropped in level over a one-mile distance of telephone wire.

The decibel scale is often used to express the signal to noise ratio, frequency and amplitude response limits in the majority of instrument specifications. The main application is, however, in the acoustic field to define response limits in audio equipment and as a means of defining noise levels. In the latter case a sound pressure level is defined in decibels in which case a reference pressure of 2×10-5Pa is used as a base pressure and the pressure measured by a microphone is related to this standard base pressure.

The logarithmic nature of the decibel allows us to compare two values of enormously different magnitudes with conveniently small numbers. e. g. the limits of hearing in terms of absolute pressure level cover the range from 20µPa to 200,000,000 µPa. The same range expressed in dB SPL is 0 -140 dB SPL. This is much more convenient.

A difference of 20 dB between two sounds means that the more intense one has 10 times the amplitude (100 times the power) of the softer. A change of 3dB is commonly thought to be the smallest change in sound pressure level that can be remembered.

Note: whenever quoting any level as a dB care should be taken to specify the reference level. In acoustics this is often dropped.

Acousticians use the dB scale for the following reasons:

• Quantities of interest often exhibit such huge ranges of variation that a dB scale is more convenient than a linear scale. For example, sound pressure radiated by a submarine may vary by eight orders of magnitude depending on direction.
• The human ear interprets loudness on a scale much closer to a logarithmic scale than a linear scale.
 Change in Sound Pressure Level dB Approximate change in acoustic pressure percentage change in acoustic pressure Human Subjective Reaction 1dB 1.1 10% Can′t detect 3dB 1.4 40% Minimum change we can remember 6dB 2.0 100% Pressure doubling, significant change 10dB 3.3 330% Subjective doubling 20dB 10.0 1000% Very noticeable change

dB(A) – a sound-level meter reading with an A-weighting network simulating the human-ear response at a loudness level of 40 phons.

 Noise Source Sound Pressure Level dB(A) Jet takeoff from 25m (possible eardrum damage) 150 Aircraft carrier flight deck 140 Jet take-off from 100m 130 Rock band 110 – 120 Jet fly-by at 300m, car horn at 1m 100 – 110 Petrol grass mower – operator 90 – 100 Food blender – operator, busy urban street 80 – 90 Accelerating vehicle from 50kmhr-1 at 7.5m 70 – 80 Vacuum cleaner – operator 60 – 70 Light traffic at 30m 50 – 60 Quiet residential area – daytime 40 – 50 Quiet residential area – nighttime 30 – 40 Wilderness, rustling leaves, whisper 20 -30 Breathing 10 Threshold of human hearing 0

Measurement – there are a number of points that should be taken into account when measuring sound pressure level:

1. measurement point in space relative to equipment being measured and/or surrounding environment.
• Sensitivity of location
• Operating condition and stability of equipment being measured
2. dynamic range and frequency limitations of microphone and measuring equipment versus test requirements
• document for future reference
• compared to post processing requirements
3. calibration of microphone
• calibration may need to be performed before and after measurement
• calibration frequency and level versus measurement requirements

A-Weighting – This is the most generally used filter when making overall noise measurements. The attenuation of the sound signal with an A-weighted filter corresponds to the fact that the human ear is not as sensitive to sound of the lower frequencies as it is at the higher frequencies.

The A-Weighted Sound Level is a single number measure of the relative loudness of noise that is used extensively in outdoor environmental noise standards. The ratings correlate well with human judgments of relative loudness, but do not take into account the spectral balance or sound quality. Many different sounding spectra can result in the same numeric value, but have quite different subjective qualities. The A-Weighted Sound Level can be measured with simple sound level meters; the rating is expressed as a number followed by dB(A) or dBA. For example, 35dB(A).

The A weighting curve approximately follows the equal loudness curve of 40 phons.

The 40 phon curve shown in red and the inverted (40dB-A weighting) A-weighting curve shown in blue.

The inverted A weighting curve was calculated based on the fact that the A-weighting is 0dB at 1000Hz and the 40 phon curve is 40dB at 1000Hz, therefore, these two points coincide.

A-weighted levels are not a suitable descriptor for low frequency noise 20 to 200Hz. A-weighted sound pressure level has been found to be an unsatisfactory descriptor to predict effects caused by low frequency noise. According to previous studies, specific sound characteristics that are not fully assessed by an A-weighted sound pressure level could be of importance for adverse effects of low frequency noise.

The A-weighting value in decibels as a funcion of frequency is given by:

where

WA = weighting to be applied, dB

f = frequency, Hz