Page 44 - Master Handbook of Acoustics

CHAPTER 2

Sound Levels and the Decibel

T he decibel is one of the most important units of measure in the field of audio. The decibel

provides an extraordinarily efficient way to describe audio phenomena and our perception of

them. In this chapter we explore the decibel concept and see how decibels can be used to measure
sound levels in various applications. Several numerical examples demonstrate the mathematics
needed to use decibel measurements.
Sound levels expressed in decibels clearly demonstrate the wide range of sensitivity in human
hearing. The threshold of hearing matches the ultimate lower limit of perceptible sound in air, that is,
the noise of undisturbed air molecules bumping against the eardrum. At the other end of the range, the

ear can tolerate very high intensities of sound; at these sound levels, hearing damage is a very real
possibility. A sound level expressed in decibels is a convenient way of handling the billion-fold
range of sound pressures to which the ear is sensitive.

Ratios versus Differences

Imagine a sound source set up in a room completely protected from interfering noise. The sound
source is adjusted for a weak sound with a sound pressure of 1 unit, and its loudness is carefully
noted.
In observation A, to double the perceived loudness, the sound pressure must be increased from 1

to 10 units. The source pressure is now adjusted to 10,000 units. For observation B, to again double
the perceived loudness, we find that the sound pressure must be increased from 10,000 to 100,000
units. The results of this experiment can be summarized as follows:

Observations A and B accomplish the same doubling of perceived loudness. In observation A, this
was accomplished by an increase in sound pressure of only 9 units, whereas in observation B an

increase of 90,000 units was required. Ratios of pressures seem to describe loudness changes better
than absolute differences in pressure. Early acoustics researchers including Ernst Weber, Gustaf
Fechner, and Hermann von Helmholtz demonstrated the importance of using ratios in such
measurements. Ratios apply equally well to sensations of vision, vibration, or even electric shock.
Ratios of stimuli come closer to matching human perception than do absolute differences of stimuli.

This matching is not perfect, but close enough to make a strong case for expressing sound levels in