Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
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measured as a displacement above or below equilibrium atmospheric pressure. During audio
recording, a microphone measures this constantly changing air pressure amplitude and converts
it to electrical units of volts (V), sending the voltages to the sound card for analog-to-digital
conversion. We'll see below how and why all these units are converted to decibels.
The objective measures of intensity and air pressure amplitude relate to our subjective
experience of the loudness of sound. Generally, the greater the intensity or pressure created by
the sound waves, the louder this sounds to us. However, loudness can be measured only by
subjective experience that is, by an individual saying how loud the sound seems to him or her.
The relationship between air pressure amplitude and loudness is not linear. That is, you can't
assume that if the pressure is doubled, the sound seems twice as loud. In fact, it takes about ten
times the pressure for a sound to seem twice as loud. Further, our sensitivity to amplitude
differences varies with frequencies, as we'll discuss in more detail in Section 4.1.6.3.
When we speak of the amplitude of a sound, we're speaking of the sound pressure
displacement as compared to equilibrium atmospheric pressure. The amount of displacement
from equilibrium is actually very small, even for the loudest sounds we listen to. However, the
range of the quietest to the loudest sounds in our comfortable hearing range is actually quite
large. The loudest sounds are on the order of 20 Pa. The quietest are on the order of 20 Pa,
which is 20
10-6
Pa. (These values vary by the frequencies that are heard.) Thus, the loudest
has about 1,000,000 times more air pressure amplitude than the quietest. Since intensity is
proportional to the square of pressure, the loudest sound we listen to (at the verge of hearing
damage) is times more intense than the quietest. (Some
sources even claim a factor of 10,000,000,000,000 between loudest and quietest intensities. It
depends on what you consider the threshold of pain and hearing damage.) This is a wide
dynamic range for human hearing.
Another subjective perception of sound is pitch. As you learned in Chapter 3, the pitch
of a note is how "high" or "low" the note seems to you. The related objective measure is
frequency. In general, the higher the frequency, the higher is the perceived pitch. But once
again, the relationship between pitch and frequency is not linear, as you'll see below. Also, our
sensitivity to frequency-differences varies across the spectrum, and our perception of the pitch
depends partly on how loud the sound is. A high pitch can seem to get higher when its loudness
is increased, whereas a low pitch can seem to get lower. Context matters as well in that the pitch
of a frequency may seem to shift when it is combined with other frequencies in a complex tone.
Let’s look at these elements of sound perception more closely.
4.1.4 Units for Measuring Electricity and Sound
In order to define decibels, which are used to measure sound loudness, we need to define some
units that are used to measure electricity as well as acoustical power, intensity, and pressure.
Both analog and digital sound devices use electricity to represent and transmit sound.
Electricity is the flow of electrons through wires and circuits. There are four interrelated
components in electricity that are important to understand:
potential energy (in electricity called voltage or electrical pressure, measured in volts,
abbreviated V),
intensity (in electricity called current, measured in amperes or amps, abbreviated A),
resistance (measured in ohms, abbreviated ), and
power (measured in watts, abbreviated W).
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