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I. MECHANICS OF SOUND TRANSMISSION

Objectives

In order to understand how the ear functions we need to know something about what a sound is and how it behaves. This section of the module introduces some basic properties of sound waves and provides a necessary background for understanding normal hearing and hearing impairment. At the end of this section you should be able to:

1. State what constitutes a sound wave

2. State the parameters of a sinusoidal sound wave, defining what is meant by frequency, sound pressure, period and wavelength

3. Define the decibel notation

4. Describe the sensitivity of the ear and how that sensitivity is measured

5. Draw the axes of an audiogram and describe how the audiogram is used to evaluate hearing

MECHANICS OF SOUND TRANSMISSION

Objective 1: What is sound?

The vibration of an object, a sound source, causes waves to be transmitted through air (usually) to our ears. It is this undulatory motion of air particles that triggers a cascade of mechanical and electrical events leading, ultimately, to the sensation of hearing. While we usually consider sound waves in air, they can propagate through any elastic medium, as we will describe when we take up the action of the inner ear. In order to understand how the ears and brain process sound information, we need to know something about what a sound is and how it is produced.

Air particles are in constant random motion, exerting very small pressure variations around the steady-state atmospheric pressure. Each particle is subject to both an inertial force (due to its mass and acceleration) and a force which tends to restore the particle too its resting position (due to the elasticity of the medium). When an object (such as a loudspeaker cone) is set into vibration, each air particle moves to and fro about its average position along an axis parallel to the direction in which the wave propagates. Figure 1 is intended to show the spatial distribution of pressure increases (condensations) and pressure decreases (rarefactions) of the particles throughout the medium at a given instant in time created by the vibrating object. For sinusoidal vibration, the distance between succesive peaks is called the wavelength.

Air particles themselves do not move very far, they simply transfer pressure changes by what is referred to as sound propagation. This constitutes what we call a 'sound wave' which moves away from the sound source at a velocity determined by the medium. The velocity of propagation of a sound wave in air is about 344 meters per second while in water it is 1437 m/s. Above the dot pattern shown in Figure I-1 is a curve which plots the instantaneous differential pressure throughout the medium at one instant in time for a sinusoidal vibration. Such a vibratory pattern is heard as a pure tone.


Fig. I-1) Distribution of air particles when a sound source is vibrated as afunction of distance in the direction of sound propagation.

Sound waves move out spherically from a point source of sound (Fig. I-2). As they do so they become less intense. This is because with a source emitting constant power the area of the surface of the sphere increases, thus sound intensity at any point on the sphere must decrease. Sound pressure is inversely proportional to distance from the source as long as the sound does not encounter obstacles, like the head and external ears for example.

Obstacles, which create a change in the medium, impede or resist the propagation of sound. When a sound waved encounters a change in medium, and thus in impedance, a portion of the sound wave is reflected from the surface. That portion not reflected is absorbed and continues to be propagated through the new medium. This is important to remember, for it is at the heart of our understanding of the action of the middle ear, whose purpose is to overcome the impedance mismatch of air and fluid (of the inner ear).

Reflected sound may encounter the original sound wave and, depending on the relative timing of the two, they may either reinforce or cancel one another. This is important with repect to the way in which the head and external ears alter incoming sound waves.

Sound waves may also be diffracted, which means that, depending on the frequency of the sound, they are able to wrap around small or medium-size objects (like the head for example). This can create a 'sound shadow', and is very important when we consider binaural (two-ear) hearing.

Objective 2: How do we describe a sound? What are its parameters?

Sound is described as loud or soft, high pitched or low, rough or smooth, etc. The fundamental physical descriptors of a sound are its frequency and its intensity. These translate into the psychological attributes of pitch and loudness, respectively.

We could use any of several physical quantities to describe the strength of a sound wave, but it is most convenient to use sound pressure, which is the extremely small alternating deviation above and below atmospheric pressure due to the propagated wave of compression and rarefaction. A useful stimulus for testing auditory function is a pure tone for which the sound pressure is a sine wave when plotted against time, as shown in Figure I-3.

The frequency of a pure tone is the number of cycles or complete oscillations of condensation and rarefaction in one second. The unit of measurement is Hertz (Hz). Thus, a pure tone that goes through 1000 cycles per second has a frequency of 1000 Hz, or 1 kHz (kiloHertz).

The period of a pure tone is the time required for one complete cycle, or the time that elapses between two successive condensation or rarefaction peaks. The period is thus arithmetically equal to the reciprocal of the frequency.

period (t) = 1/ frequency (f)

When plotted on a scale of distance (Fig. 1) the wavelength is the distance between two successive peaks on the wave; it may be calculated by dividing the velocity of wave propagation by the frequency.

wavelength (g) = velocity (v)/ frequency (f)

Objective 3: How do we measure the strength of a sound. The Decibel notation

Because the ear operates over a range of sound pressures (its dynamic range) which is greater than a million to one, stimulus strength is usually expressed in logarithmic units known as decibels (dB). The decibel notation always expresses the ratio between two intensities. When stimulus strength is expressed in terms of sound pressure, the following relationship is used, where P1 and P2 are two sound pressures. For studies of hearing, P2 is taken as the sound pressure at the threshold hearing of a normal listener.

dB = 20 log10 (P1/P2)

If, for example, the sound pressure from one source (P1) is is ten times greater than that from a second (P2), the difference is 20 dB.

dB = 20 log10 (10/1) = 20 x 1 = 20

The sound pressure of a very loudsound, such as a jet plane, may be one million times (106) the pressure of the weakest sound that can be detected by someone with normal hearing; these two sounds differ by 120 dB:

20 log10 (P1/P2) = 20 log10 106 = 20 x 6 = 120 dB

The chart below shows on a dB scale the sound pressure level of sounds common to our everyday environment.

Objective 4: Sensitivity of hearing

Figure I-4 illustrates the amazing sensitivity of the ear. The curve shows the threshold of hearing (left axis) and the amplitude of vibration of the eardrum (right axis) at the threshold of hearing at various frequencies. There are several important things to notice about this curve. First, the threshold of hearing varies with frequency of the sound; the ear is most sensitive around 4 kHz. Second, at the most sensitive frequency around 4 kHz the amplitude of motion of the eardrum is about 10-9 cm, which is only about 1/10 the diameter of a hydrogen atom. Thus, the ear is extraordinarily sensitive, operating in therange of atomic motion.

This almost unbelievable degree of sensitivity is even more impressive when account is taken of the fact that the receptor mechanisms in the inner ear operate in a fluid environment, i.e., the inner ear is really an "underwater" sound receiver. When sound in air strikes a fluid boundary (a boundary between media with different acoustic impendances) there is a theoretical loss of 99.9% of the energy (due to reflection). This 99.9% loss is equivalent to 30 dB; a reduction in stimulus intensity of this amount is quite noticeable to a listener. We shall consider some of the mechanisms that act to overcome this potential loss and increase auditory sensitivity.

We also note on the graph the frequencies and sound pressure levels associated with normal conversational speech. This region is situated to allow for considerable range of modulation of speech intensity.

Objective 5: The Audiogram - a basic clinical test of hearing sensitivity

For convenience in describing the hearing sensitivity of patients in the audiologic clinic, the number of dB by which the threshold sound pressure of an individual exceeds the normal threshold is referred to as dB of "hearing loss."

A graph of "hearing loss" vs. frequency is known as an audiogram. The audiogram (Figure I-5) illustrates a gradually sloping hearing loss that would become quite noticeable to the listener at frequencies above 500 Hz. We will return to audiograms and how they help us understand the mechanisms of hearing loss later in this section.

Fig. I-5

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