time (s)
f1
f2 f3
frequency (Hz)
Figure 3: A slightly more complex sound
is affected by the distance from the source and by the acoustic surroundings. The range of sound powers (and resulting sound pressures) is very large – from a whisper at 10-9 rocket at 106
W. Human sound perception
does not vary linearly with the intensity – intensity being the amount of sound power per unit area (W·m-2
time (s) frequency (Hz) Figure 4: Octave band frequency analysis
simple waveform in Figure 3 could be resolved into three frequencies, each with their own strength. In the real world, there are sounds that
are said to be ‘continuous’, such as that shown in Figure 4. This is made up of many frequencies that make it practically impossible to break it up into discrete pure tones. In order to represent this type of sound, which is very common, the frequencies are measured in ‘bands’ (similar concept to ‘bins’ in external temperature assessments). These bands (that may be ‘octave’ or ‘1/3 octave’ bands) more readily visualise the characteristic of the sound by losing the detail of individual frequencies. The use of octave band analysis must be employed with care, since there may be peaks of frequencies that occur within the band that will be ‘levelled out’ by the averaging effect within a complete band.
In the hearing range, perceived loudness is critical in the assessment of the acoustic environment, as this will infl uence the design and operation of systems so that they do not adversely affect people
The actual strength of a particular sound
felt by the ear is related to the fl uctuations of sound pressure (Pa) reaching the ear. The strength of the source itself is determined by the sound energy output, known as sound power (W), and for a piece of equipment would typically be assessed in a test chamber. The sound power is an attribute of the item that is generating the sound (such as a fan), and is normally assumed constant for a piece of equipment regardless of location. However, the sound pressure is related to the position of the listener relative to the sound source, and
66 CIBSE Journal March 2012 would not perceive a 1015
) – and the listener -fold difference
between the whisper and a rocket but relate it to their threshold of hearing in a way that is similar to a logarithmic scale. So, to better represent the ear’s response to sound, and to allow the manipulation of these numerically disparate values, logarithms are typically used. The threshold of hearing corresponds to
a pressure variation less than a trillionth of atmospheric pressure, and to refl ect this, a reference sound power (or datum) is taken as 10-12
W (1 pW), and the sound power
level is calculated relative to this. sound power level, LW =
10 log10 sound power reference sound power decibels (dB)
The value of the ‘Bel’ is given by the log (to base 10) of the ratio of two quantities – in this case, two sound powers. The ‘decibel’ is a tenth of a Bel (hence the multiplier ‘10’ in the equation) and provides a more usable scale – the Bel is not used in acoustics. So, for example, if a fan has a sound
power of 0.001 W, the sound power level would be
10 log10 10-3 10-12 = 10 log10109 = 90 dB
As the ear responds to sound intensity I, where I = p2 (kg·m-3 (m·s-1
/ρc and ρ is the air density
) and c is the speed of sound ), the sound pressure level uses a
ratio of the square of the sound pressure to provide a usable and relevant metric for sound pressure. So, sound pressure level, LP =
10 log10 = 20 log10
(reference sound power)2 decibels (dB) p
(sound pressure)2 pref decibels (dB)
and Pref is the pressure at the lower end of human audibility 2 x 10-5
Pa (or 20 µPa)
So, for example, in the middle of a library, if the sound pressure is 1.2 x 10-3
Pa, the
sound pressure level, LP = 20 log10
1.2 x 10-3 2 x 10-5
= 36 dB
A 3 dB change in sound pressure level is just noticeable, a 5 dB change clearly noticeable, and a 10 dB change is twice (or half) as loud.
W through to a space
If there is more than one source of
sound in a room, then the sound pressure level may be added together by fi rst converting back to the square of sound pressure, adding and then reconverting back to dB or, rather more easily (but approximately), the table below may be used to add the different sources together.
If the levels to be added differ by… (dB)
0 or 1 2 or 3 4 to 9
10 or more
The total is the larger level plus… (dB)
3 2 1 0
Figure 5: Approximate method of adding dB sound sources together
So, for example, if one source has a sound pressure level of 45 dB and another 46 dB, the difference is 1 dB, and so the overall sound pressure level is (46 + 3) = 49 dB. The ear does not respond equally to
all frequencies. This appreciation of loudness is refl ected in the phon scale, as shown in Figure 6. For example, a 50
phon contour would show values of LP for other frequencies that are perceived equally loud as 50 dB at 1,000 Hz, and looking at a frequency of 100 Hz, a
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pressure (Pa)
pressure (Pa)
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