Technical Article

Explanatioin of decibel levels

By Jeremy Tatum, Ph.D.

In physics, the intensity of a sound is best expressed by the rate at which energy is received per unit area, in watts per square metre (W m-2).

The decibel scale is a logarithmic scale, such that for every ten-fold increase in intensity, there is a difference of 1 bel, or 10 decibels, in the decibel level. Mathematically, if the intensities of two sounds are in the ratio *I*2/*I*1, the difference in their decibel levels is given by

If one air-conditioner has an intensity of *I* watts per square metre, then four air-conditioners will have an intensity of 4*I *watts per square metre. If one of them has a decibel rating of 80 dB, then decibel level *D* of four of them will be given by

Now the logarithm of 4 is 0.602, so the decibel level of the four air-conditioners will by given as

so that *D *is approximately 86 dB.

To a good approximation, for every doubling of the sound intensity, the decibel level increases by 3 dB.

The situation is complicated if you have four rather large machines in a small confined space, and it is further complicated when you are concerned with the “perceived decibel level”, since you are then concerned with the physiological response of the ear to sound, and to the psychological annoyance of noise. While the subject then starts to become quite complicated, to a rough approximation the response of the ear is logarithmic, so that you can take it that an increase in 3 dB corresponds to a doubling in the noise intensity.