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The decibel is one of the most important units of measure in the audio field. The decibel is an extraordinarily efficient way to describe audio phenomena, and our perception of them. 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, the noise of air molecules against the eardrum. At the other end of the range, the ear can tolerate very high intensities of sound. A level expressed in decibels is a convenient way of handling the billion-fold range of sound pressures to which the ear is sensitive. Ouns intensity is difficult to measure (more difficult than , say, sound pressure), so it is oftentimes useful to express sound intensity in ratios, as ratios apply equally well to sensations of vision, hearing, vibration, or even electric shock. Ratios of stimuli come closer to matching human perception than do differences of stimuli. This matching is not perfect, but close enough to make a strong case for expressing levels in decibels. Ratios of powers or ratios of intensities, or ratios of sound pressure, voltage, current, or anything else are dimensionless. Sound intensities are generally expressed as logarithms (base 10) of the ratios. Logarithms are outside the scope of this class, but if you wanted to understand them more fully, you can find some information here.
Reference levels are widely used to establish a baseline for measurements. For example, a sound-level meter is used to measure a certain sound-pressure level. If the corresponding sound pressure is expressed in normal pressure units, a great range of very large and very small numbers results. As we have seen, ratios are more closely related to human perception than linear numbers, and by expressing levels in decibels, we compress the large and small ratios into a more convenient and comprehensible range.
The human hearing response is not flat across the audio band. For example, our hearing sensitivity particularly rolls off at low frequencies, and also at high frequencies. Moreover, this roll-off is more pronounced at softer listening levels.
Sound in the Free Field
Many practical acoustic problems are invariably associated with structures such as buildings and rooms, and vehicles such as airplanes and automobiles. These can generally be classified as problems in physics. These acoustical problems can be very complex in a physical sense; for example, a sound field might be comprised of thousands of reflected components, or temperature gradients might bend sound in an unpredictable manner. In contrast to practical problems, the simplest way to consider sound is in a free field, where its behavior is very predictable and analysis is straightforward. This analysis is useful because it allows us to understand the nature of sound waves in this undisturbed state. Then, these basic characteristics can be adapted to more complex problems.
Sound in a free field travels in straight lines and is unimpeded. Sound in a free field is unreflected, unabsorbed, undeflected, undiffracted, unrefracted, undiffused, and not subjected to resonance effects. Generally, a free field is a theoretical invention, a free space that allows sound to travel without interference. Approximations exist, however, such as those found within anechoic chambers.
Consider the point source of Fig. 3-1, radiating sound at a fixed power. The source can be considered as a point because its largest dimension is small (perhaps one-fifth or less) compared to the distances at which it is measured. For example, if the largest dimension of a source is 1 ft, it can be considered as a point source when measured at 5 ft or farther. Looked at in another way, the farther we are from a sound source, the more it behaves like a point source. In a free field, far from the influence of reflecting objects, sound from a point source is propagated spherically and uniformly in all directions. In addition, as described below, the intensity of sound decreases as the distance from the source increases.
This sound is of uniform intensity (power per unit area) in all directions. The circles represent spheres having radii in simple multiples. All of the sound power passing through the small square area A1 at radius r also passes through the areas A2, A3, and A4 at radii 2r, 3r, and 4r, respectively. The same sound power flows out through A1, A2, A3, and A4, but an increment of the total sound power traveling in this single direction is spread over increasingly greater areas as the radius is increased. Thus, intensity decreases with distance. This decrease is due to geometric spreading of the sound energy, and is not loss in the strict sense of the word.
Similarly, sound pressure follows an inverse law,
For every doubling of distance r from the sound source, sound pressure will be halved (not quartered). This is only true for a free field in which sound diverges spherically, but this procedure may be helpful for rough estimates even under other conditions.