Pressure
1 Atmosphere = 14.7PSI, 1.0133 bar, 101.33 kPa, 101330 Pascals (Pa) or Newtons m-2
Force
F =mass x acceleration in kg x (m/s2), measured in Newtons (N)
Realisation of the Unit of Sound Pressure
All audiometric measurements are derived from sound pressure. It is
not practical to maintain a standard source which generates a Pascal
of sound pressure, but instead, all acoustical measurements are traceable
through accurately calibrated microphones.
Knowing the relationship between the sound pressure on the membrane
of a microphone and the output voltage at its electrical connector
defines its sensitivity, and is the foundation of sound measurement.
The transmission constant of a laboratory standard microphone is determined
by means of the Reciprocity Method (below) (IEC 1094, Part 2). The
acoustic unit, the Pascal, is derived from mechanical and electrical
units. Reproduction of the standard Pascal is achieved indirectly:
Using sound calibrators and standard microphones provides means of
traceability back to sound pressure standards.
Reciprocity method:
The Reciprocity Method relies on the ability of a condenser microphone to be used as a sound source as well as a sound receiver. The energy conversion sensitivity of the microphone when it is used as a transmitter is the same as its receiving sensitivity. If two microphones are coupled acoustically, the product of their sensitivities can be found by measurement of the transmitter microphone drive current, the coupler impedance and the receiving microphone voltage output. In a well designed apparatus, the transmit drive current and the acoustic coupling impedance can be made constant, so the only variable will be the output voltage of the receiver, thus simplifying the procedure. If a set of three microphones is used, each as a transmitter and receiver in a three way comparison, the relative sensitivity of each microphone can be defined. A system of traceable microphones and measuring systems is used to produce known microphones with a sensitivity related to sound pressure standards having an error of less than 0.1dB over most of the audio spectrum.
The Reciprocity Method was established as the primary standard for
acoustics by IEC 327 circa the 1970’sAn excellent discussion
of the history of acoustic standard development and other topics can
be found at the National Physical Laboratory, UK
Sound Pressure Level (SPL) and Sound Perception
Sound Pressure Level, SPL, is sound pressure expressed in dB referenced to 20 micro Pascals (20µPa), the “threshold of hearing”.
Sound Pressure Level, dB ref 20µPa (dB20µPa ) = 20.log10(Sound Pressure/20µPa).
Or add 20dB for every 10-fold increase in sound pressure.
The entire human hearing range lies between 0 and 120dB SPL
Airborne sound is defined as variation in air pressure, which at
sea level is an average of 101325 Pascal (Pa). The human ear can
perceive pressure variations between the hearing threshold of 0.00002
Pa (20µPa ) and the pain threshold of 20 Pa. The ear can therefore
cope with a pressure range of 1:1 million! The weakest sound the
human ear can detect is a change of 20µPa, which causes the
eardrum to be deflected “less than the diameter of a hydrogen
molecule”.
- B&K “Measuring Sound”.
Normal Equal Loudness Contours For Pure Tones
The threshold of hearing was charted along with equal loudness contours by Fletcher & Munsen in the 1930’s (Ref “AS 3657.1 1989 p6.) Perceptually all the sounds corresponding to the points on one of the Equal Loudness Contours have the same intensity. Reduced sensitivity and more difficult discrimination of differences in intensity at lower frequencies are due to the disproportionate scale of the ear verses wavelength. The upper frequency limit is related to ear component resonances. |
 Equal loudness contours |
Weighting Scales
When this was discovered, it was clear that in order to objectively measure the sensation of sound, a matching filtering network was required. But since the ear exhibits an increasingly compressed response at higher levels, several weighting scales had to be defined. The scales approximate the inverted Equal Loudness Contours, the most commonly used scales are shown. “A” weighting - dBA - is intended for low level sounds “B” for medium, & “C” for high.
| Attempts were made to produce a scale of sound by comparison
with a pure 1kHz tone – the “phon”, which
equals the sound pressure level (in unweighted decibels).
This failed because it was found that the results did not
constitute an actual scale of loudness e.g. 80 phon is not
twice as loud as 40 phon. |
 A, B & C weighting scales |
There are some practical problems using these weighting filters:
- You have to know what range to use in order to select the appropriate weighting before you take the final reading.
- The Fletcher Munsen curves are only a statistical representation of Otological normalcy, -not representing the actual response of an individual
- The curves were developed using pure tones, -not representing typical complex sounds.
The A weighting scale is still widely used because of its simplicity. Studies have shown that there is a good correlation between A-weighted sound level and hearing damage, even though the scale is intended for low level sounds, while hearing damage is often associated with exposure to loud sounds. The A-weighted sound level is the best single-figure guess available for assessing noise problems and making decisions. It also exhibits a reasonable correlation with the tendency for people to complain of noise pollution.