Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
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well as the air pressure amplitude changes detected by microphones and translated to voltages.
Power, intensity, and pressure are valid ways to measure sound as a physical phenomenon.
However, decibels are more appropriate to represent the loudness of one sound relative to
another, as well see in the next section.
4.1.5 Decibels
4.1.5.1 Why Decibels for Sound?
No doubt you’re familiar with the use of decibels related to sound, but let’s look more closely at
the definition of decibels and why they are a good way to represent sound levels as they’re
perceived by human ears.
First consider Table 4.1. From column 3, you can see that the sound of a nearby jet
engine has on the order of times greater air pressure amplitude than the
threshold of hearing. That’s quite a wide range. Imagine a graph of sound loudness that has
perceived loudness on the horizontal axis and air pressure amplitude on the vertical axis. We
would need numbers ranging from 0 to 10,000,000 on the vertical axis (Figure 4.1). This axis
would have to be compressed to fit on a sheet of paper or a computer screen, and we wouldn't
see much space between, say, 100 and 200. Thus, our ability to show small changes at low
amplitude would not be great. Although we perceive a vacuum cleaner to be approximately
twice as loud as normal conversation, we would hardly be able to see any difference between
their respective air pressure amplitudes if we have to include such a wide range of numbers,
spacing them evenly on what is called a linear scale. A linear scale turns out to be a very poor
representation of human hearing. We humans can more easily distinguish the difference
between two low amplitude sounds that are close in amplitude than we can distinguish between
two high amplitude sounds that are close in amplitude. The linear scale for loudness doesn’t
provide sufficient resolution at low amplitudes to show changes that might actually be
perceptible to the human ear.
Figure 4.1 Linear vs. logarithmic scale
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