Sound Intensity Level (SL)

These size-of-domain difficulties are avoided if we use a logarithmic scale based on a ratio of intensities. As it happens, we are normally more interested in comparing intensities than dealing with absolute values. This comparison is achieved by observing their ratio. For example, if the ratio of the intensities of two sounds is 3, one intensity is thrice that of the other.

Instead of specifying the power density (intensity) itself it is customary to specify how many times the actual power is greater than the power of a reference-level soundwave. This reference level is
10 Watt/m. This is about the weakest sound that humans can hear. The intensity of a sound above this reference level is the Sound Intensity Level(SL) of the sound.

If one sound has an intensity ( in Watt/m) and a second sound has an intensity , the second has an intensity relative to the first of /. The log of this ratio gives us a value for the relationship, the unit being the bel after Alexander Graham Bell, the inventor of the telephone.


The human audible range is then A still more practical unit of sound intensity level, SL, that is used more widely today, is the tenth part of a bel, the decibel (dB).

where = 10 Watt/m, the intensity at the threshold of hearing. functions as a reference intensity - i.e. larger intensities are compared to through the ratio /.

Calculation of some useful Sound Levels (SL's, in decibels)

1. Threshold of Feeling - SL of I =

N.B. The scale of SL's has been compressed from between 10 watt/mand 1 watt/mto between 0 and 120 dB - which is much more convenient.

2. Threshold of Hearing - SL of I = 10 watt/m

3. "Fortissimo" - SL of I = 10 watt/m

4. "Pianissimo" - SL of I = 10watt/m

5. Doubling The Sound Intensity Level

What is the change in SL when the intensity, I, is doubled?

Sound Intensity Level and Distance

If a sound is not reflected or interrupted, the intensity drops 6 dB ( i.e. 0.25 of its value) every time we double the distance. Thus, if the SL is 90 dB at 2 metres from the source, it will be 84 dB at 4 metres and 78 dB at 8 metres.