Section 12.3
Section 12.3 Hearing and the EarFIGURE 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 SoundFIGURE 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 EarFIGURE 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 threshold of
pain, 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 SoundTABLE 12.1 Sound Levels Due to VariousSources (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