Elements of the Description - The Physics of Birdsong - page 9

1.2.2 Intensity of Sound

In the previous section, we were able to define the units of the period and the
frequency. Now that we have a description of the nature of the sound pertur-
bation, we shall concentrate on its amplitude . For a periodic wave such as the
one displayed in Fig. 1.3b, the amplitude is the number that measures the
maximum value of the departure from the average of the oscillating quantity.
Since, for a gas, the pressure is a function of the density, we can perform
a description of the sound in terms of the fluctuations of either quantity.
Traditionally, the option chosen is to use the pressure. Therefore, we have
to describe how much the pressure P varies with respect to the atmospheric
pressure P 0 when a sound wave arrives. Let us call this pressure p (that is,
the increment of pressure when the sound wave arrives, with respect to the
atmospheric value), and its amplitude A . Now, the minimum value of this
quantity that we can hear is tiny: only 0 . 00000000019 times atmospheric pres-
sure. Let us call this the reference pressure amplitude A ref . We can therefore
measure the intensity of a sound as the ratio between the sound pressure
amplitude when the wave arrives, A , and the reference pressure amplitude
A ref .
This strategy is the one used to define the units of sound intensity. How-
ever, since the human ear has a logarithmic sensitivity (that is, it is much
more sensitive at lower intensities), the sound intensity is measured in deci-
bels (dB), which indicate how strong a pressure fluctuation with respect to a
reference pressure is, but the intensity is measured in a way that reflects this
way of perceiving sound. The sound pressure level I is therefore defined as

I =20log 10 ( A/A ref ) . (1.10)

A sound of 20 dB is 10 times as more intense (in pressure values) as the
weakest sound that we can perceive, while a sound of 120 dB (at the threshold
of pain) is a million times as intense.
In Fig. 1.4, we show a series of familiar situations, indicating their charac-
teristic frequencies and intensities. For example, a normal conversation has a
typical intensity of 65 dB, and a rock concert can reach 115 dB (close to the
sound intensity of an airplane taking off at a distance of a few meters, and
close to the pain threshold). In terms of frequencies, the figure begins close
to 20 Hz, the audibility threshold for humans. Close to 500 Hz, we place a
note sung by a baritone, while at 6000 Hz we locate a tonal sound produced
by a canary.

1.3 Harmonics and Superposition

1.3.1 Beyond Frequency and Amplitude: Timbre

We can tell an instrument apart from a voice, even if both are producing
the same note. What is the difference between these two sounds? We need