Section 12.3
Hearing and the Ear FIGURE 12.6 An uncoiled view of the cochlea.
12.3.1 Performance of the Ear
The nerve impulses evoke in the brain the subjective sensation of sound.
Loudness, pitch, and quality are some of the terms we use to describe the sounds we hear. It is a great challenge for physiologists to relate these subjective responses with the physical properties of sound such as intensity and frequency. Some of these relationships are now well understood; others are still subjects for research.
In most cases, the sound wave patterns produced by instruments and voices are highly complex. Each sound has its own characteristic pattern. It would be impossible to evaluate the effect of sound waves on the human auditory system if the response to each sound pattern had to be analyzed separately.
Fortunately the problem is not that complicated. About 150 years ago, J. B.
J. Fourier, a French mathematician, showed that complex wave shapes can be analyzed into simple sinusoidal waves of different frequencies. In other words, a complex wave pattern can be constructed by adding together a sufficient number of sinusoidal waves at appropriate frequencies and amplitudes.
Therefore, if we know the response of the ear to sinusoidal waves over a broad range of frequencies, we can evaluate the response of the ear to a wave pattern of any complexity.
An analysis of a wave shape into its sinusoidal components is shown in Fig. 12.7. The lowest frequency in the wave form is called the fundamental, and the higher frequencies are called harmonics. Figure 12.8, shows the sound pattern for a specific note played by various instruments. It is the harmonic content of the sound that differentiates one sound source from another.
Chapter 12
Waves and Sound FIGURE 12.7 The analysis of a complex wave shape (a), into its sine components (b). The point-by-point addition of the fundamental frequency sine wave and the harmonic frequency sine waves yields the wave shape shown in (a).
For a given note played by the various instruments shown in Fig. 12.8, the fundamental frequency is the same but the harmonic content of the wave is different for each instrument.
12.3.2 Frequency and Pitch
The human ear is capable of detecting sound at frequencies between about 20 and 20,000 Hz. Within this frequency range, however, the response of the ear is not uniform. The ear is most sensitive to frequencies between 200 and 4000 Hz, and its response decreases toward both higher and lower frequencies.
There are wide variations in the frequency response of individuals. Some people cannot hear sounds above 8000 Hz, whereas a few people can hear sounds above 20,000 Hz. Furthermore, the hearing of most people deteriorates with age.
The sensation of pitch is related to the frequency of the sound. The pitch increases with frequency. Thus, the frequency of middle C is 256 Hz, and the
Section 12.3 Hearing and the Ear FIGURE 12.8 Wave forms of sound from different musical instruments sounding the same note.
frequency of the A above is 440 Hz. There is, however, no simple mathematical relationship between pitch and frequency.
12.3.3 Intensity and Loudness
The ear responds to an enormous range of intensities. At 3000 Hz, the lowest intensity that the human ear can detect is about 10−16 W/cm2. The loudest tolerable sound has an intensity of about 10−4 W/cm2. These two extremes of the intensity range are called the threshold of hearing and the , respectively. Sound intensities above the threshold of pain may cause permanent damage to the eardrum and the ossicles.
The ear does not respond linearly to sound intensity; that is, a sound which is a million times more powerful than another does not evoke a million times higher sensation of loudness. The response of the ear to intensity is closer to being logarithmic than linear.
Because of the nonlinear response of the ear and the large range of inten sities involved in the process of hearing, it is convenient to express sound intensity on a logarithmic scale. On this scale, the sound intensity is measured relative to a reference level of 10−16 W/cm2 (which is approximately the
Chapter 12
Waves and Sound TABLE 12.1 Sound Levels Due to Various Sources (representative values)
Sound level Sound level
Source of sound (dB)
(W/cm2)
Threshold of pain
120
10−4
Riveter
90
10−7
Busy street traffic
70
10−9
Ordinary conversation
60
10−10
Quiet automobile
50
10−11
Quiet radio at home
40
10−12
Average whisper
20
10−14
Rustle of leaves
10
10−15
Threshold of hearing
0
10−16
lowest audible sound intensity). The logarithmic intensity is measured in units of decibel (dB) and is defined as Sound intensity in W/cm2 Logarithmic intensity 10 log
(12.5)
10−16 W/cm2
Thus, for example, the logarithmic intensity of a sound wave with a power of 10−12 W/cm2 is
10−12
Logarithmic intensity 10 log 40 dB 10−16 Intensities of some common sounds are listed in Table 12.1.
At one time, it was believed that the ear responded logarithmically to sound intensity. Referring to Table 12.1, a logarithmic response would imply that, for example, a busy street sounds only six times louder than the rustle of leaves even though the power of the street sounds is a million times greater.
Although it has been shown that the intensity response of the ear is not exactly logarithmic, the assumption of a logarithmic response still provides a useful guide for assessing the sensation of loudness produced by sounds at different intensities (see Exercises 12-1 and 12-2).
The sensitivity of the ear is remarkable. At the threshold of hearing, in the range of 2000–3000 Hz, the ear can detect a sound intensity of 10−16 W/cm2.
This corresponds to a pressure variation in the sound wave of only about 2.9 × 10−4 dyn/cm2 (see Exercise 12-3). Compare this to the background atmospheric pressure, which is 1.013 × 106 dyn/cm2. This sensitivity appears even more remarkable when we realize that the random pressure variations in air due to the thermal motion of molecules are about 0.5 × 10−4 dyn/cm2.
Thus, the sensitivity of the ear is close to the ultimate limit at which it would begin to detect the noise fluctuations in the air. The displacement of the molecules corresponding to the power at the threshold of hearing is less than the size of the molecules themselves.
The sensitivity of the ear is partly due to the mechanical construction of the ear, which amplifies the sound pressure. Most of the mechanical amplification is produced by the middle ear. The area of the eardrum is about 30 times larger than the oval window. Therefore, the pressure on the oval window is increased by the same factor (see Exercise 12-4). Furthermore, the ossicles act as a lever with a mechanical advantage of about 2. Finally, in the frequency range around 3000 Hz, there is an increase in the pressure at the eardrum due to the resonance of the ear canal. In this frequency range, the pressure is increased by another factor of 2. Thus, the total mechanical amplification of the sound pressure in the 3000-Hz range is about 2 × 30 × 2 120.
Because the intensity is proportional to pressure squared (see Eq. 12.3), the intensity at the oval window is amplified by a factor of about 14,400.
The process of hearing cannot be fully explained by the mechanical con struction of the ear. The brain itself plays an important role in our perception of sound. For example, the brain can effectively filter out ambient noise and allow us to separate meaningful sounds from a relatively loud background din.
(This feature of the brain permits us to have a private conversation in the midst of a loud party.) The brain can also completely suppress sounds that appear to be meaningless. Thus, we may lose awareness of a sound even though it still produces vibrations in our ear. The exact mechanism of interaction between the brain and the sensory organs is not yet fully understood.
12.4
Bats and Echoes
The human auditory organs are very highly developed; yet, there are animals that can hear even better than we can. Notable among these animals are the bats. They emit high-frequency sound waves and detect the reflected sounds (echoes) from surrounding objects. Their sense of hearing is so acute that they can obtain information from echoes which is in many ways as detailed as the information we can obtain with our sense of sight. The many different species of bats utilize echoes in various ways. The Vespertilionidae family of bats emit short chirps as they fly. The chirps last about 3 × 10−3 sec (3 msec) with a time interval between chirps of about 70 msec. Each chirp starts at a frequency of about 100 × 103 Hz and falls to about 30 × 103 Hz at the end. (The ears of bats, of course, respond to these high frequencies.) The silent interval
Chapter 12
Waves and Sound between chirps allows the bat to detect the weak echo without interference from the primary chirp. Presumably the interval between the chirp and the return echo allows the bat to determine its distance from the object. It is also possible that differences in the frequency content of the chirp and the echo allow the bat to estimate the size of the object (see Exercise 12-5). With a spacing between chirps of 70 msec, an echo from an object as far as 11.5 m can be detected before the next chirp (see Exercise 12-6). As the bat comes closer to the object (such as an obstacle or an insect), both the duration of and the spacing between chirps decrease, allowing the bat to localize the object more accurately. In the final approach to the object, the duration of the chirps is only about 0.3 msec, and the spacing between them is about 5 msec.
Experiments have shown that with echo location bats can avoid wire obsta cles with diameters down to about 0.1 mm, but they fail to avoid finer wires.
This is in accord with our discussion of wave diffraction (see Exercise 12-7).
Other animals, such as porpoises, whales, and some birds, also use echoes to locate objects, but they are not able to do so as well as bats.
12.5
Sounds Produced by Animals
Animals can make sounds in various ways. Some insects produce sounds by rubbing their wings together. The rattlesnake produces its characteristic sound by shaking its tail. In most animals, however, sound production is associated with the respiratory mechanism. In humans, the vocal cords are the primary source of sound. These are two reeds, shaped like lips, attached to the upper part of the trachea. During normal breathing the cords are wide open. To produce a sound the edges of the cords are brought together. Air from the lungs passes through the space between the edges and sets the cords into vibration.
The frequency of the sounds is determined by the tension on the vocal cords.
The fundamental frequency of the average voice is about 140 Hz for males and about 230 Hz for females. The sound produced by the vocal cords is substantially modified as it travels through the passages of the mouth and throat. The tongue also plays an important role in the final sound. Many voice sounds are produced outside the vocal cords (for example, the consonant s). The sounds in a whispering talk are also produced outside the vocal cords.
12.6
Acoustic Traps
Electronically generated sounds that mimic those of animals and insects are increasingly being used as lures to trap the creatures. Electronic fishing lures are now commercially available. One such device mimics the distress call of a mackerel and attracts marlin and other larger fish to the fishhook.