The physiology of sound

To understand a little better how we react to sound, we think it is worth reviewing some technical concepts that relate "sound" to our ears. We will see how we represent the sounds we hear numerically, so that we can then evaluate them and obtain reliable information to work with. We will review the standardized terminology used in scientific circles, as well as the differences between what is "emitted" and what is "heard". Sound is nothing more than a disturbance of the medium that produces an auditory sensation in us. There are periodic or pseudo-periodic sounds, with or without musical character, and non-periodic sounds (noise). Periodic sounds are distinguished by their pitch, their timbre and their intensity. Our magnificent ears can withstand high sound pressures (up to 1,000 microbars) and are capable of discerning sounds whose pressure differences are just 0.0001 microbars, that is, 10 million times smaller than the highest they can withstand. The frequency range of our ears, in a healthy young person, extends from 16 Hz to 20,000 Hz; we are able to analyze frequencies very selectively, to the point of being able to pick out one of them from a broad mixture.

Any body that emits vibrations (sound, if the frequency is between 16 and 20,000 Hz) that reach the tympanic membrane in our ear will cause it to vibrate at the same frequency. This vibration is transmitted, through the middle ear, to the organ of Corti, where it is converted into nerve impulses. Our brain interprets these electrical discharges as auditory sensations.



INTENSITY



As we have already mentioned, each sound differs from another in its intensity, pitch and timbre. Let's look at what each of them means. Intensity defines the energy with which a sound reaches our ear. It is related to the amplitude of the waveform with which we represent it. A pure 1 kHz tone (performing 1,000 cycles every second) has a different amplitude on the vertical axis. This difference in amplitude or, in other words, the amount of energy released, increases or decreases the energy our ears perceive; the vibration is more or less intense.

The relationship between the energy emitted and what our ears hear is not linear. We can check this by generating our own 1 kHz tone: until the loudspeaker's sound pressure level reaches a certain value, our ear will hear nothing.

For a normal ear to begin to hear something of that tone, the output power must be 10-16 W/cm2 or, in other words, 0.002 microbars or 0.20 microPa. A microbar is a pressure equal to 0.1 N/cm2 or 0.0001 pascal.

This minimum intensity is called the hearing threshold at one thousand cycles. From here, if we increase the volume level so as to perceive twice as much in this test, we observe that the output power level has increased tenfold. To increase it threefold, the power supplied by the amplifier will be 1,000 times greater than at the threshold. This is a logarithmic sensation, since there is no linear relationship between the increase in power and the sensation of loudness. To reach the hearing threshold we were applying 1 W of power, and to double the sensation of loudness we had to reach 10 W (so we have "added" 9 W of power); this does not mean that with another 9 W of power we will have a sensation of triple loudness.

The unit of measurement that relates two power levels is called the bel (B). If the ratio of two powers is 10, we can say that the difference between them is 1 bel. Since our ears are capable of perceiving differences in intensity smaller than a bel, we usually work with decibels (dB), a unit 10 times smaller.

Let's go back, in our experiment, to the threshold power level we obtained for 1 kHz. If we keep the same output power level but change the frequency of the tone we are using, we will notice that our ear seems to perceive more intensity as the tone approaches 4,000 Hz, then falls off again toward 6,000 Hz and finally disappears. If we choose to listen to what happens below

1,000 Hz, silence will take center stage. This means that the threshold intensities are different for each frequency. The graph on this page shows this threshold level for each frequency, taking a 1 kHz tone as the reference. What lies below the line indicates intensities that are inaudible to our ears. For example, at 50 Hz the threshold is 100,000 times higher than at 1 kHz.

The upper curve is that of the maximum sound intensity the human ear can bear. We note that the difference between the threshold at 1 kHz and the threshold of pain is 12 B (or 120 dB). Note that the variation of the upper curve is smaller than that of the threshold curve, from which we can deduce that differences in intensity are more critical when the power level is lower.



PITCH



If amplitude defines intensity, frequency defines pitch. Human beings are capable, though they need training, of detecting minimal differences in pitch, although it is much easier for them to discern between intensity levels. Even so, what our ears really do is look for the dominant frequency of any sound since, in the real world, there is no such thing as a pure tone (for example, the 1 kHz tone we used in the previous tests).

It is easier to group together a set of identifiable frequencies, something that is customary in music. We define an "octave" as the group of frequencies in which the last is twice the first. Thus, the 440 Hz of the note A can begin an octave that runs up to the 880 Hz of the A above.



TIMBRE



Two sounds of the same intensity and the same frequency do not sound the same to us. There is a third element that defines them: timbre. The C of a piano is not the same as the C of a violin. Why can we readily identify the source of each musical note? In the real world, as we mentioned just a few lines ago, there are no pure tones; every sound has a series of harmonics associated with it. These are what tell us that a piano or a violin is playing, or whether it is our mother or our brother speaking. The differences in the intensity of these harmonics are what define the timbre of each sound source. Harmonics are integer multiples of the fundamental frequency, that is, octaves of the primary. A sound whose fundamental is 440 Hz (the musical A) has its first upper harmonic at 880 Hz, the second at 1,760 Hz, and so on. Depending on the number of harmonics and the coherence of their intensities, we consider the sound to be more or less rich. Two supposedly identical grand pianos will show noticeable differences in these harmonics, one always being better than the other.

When a fundamental wave has harmonics that do not correspond to any multiple of it, we consider it to be noise.