Engineering Acoustics. Malcolm J. Crocker

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In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 116–127. New York: Wiley.

      4.1 Introduction

      The human ear is a marvelous and very sensitive biomechanical system for detecting sound. If it were only slightly more sensitive, we would be able to hear the Brownian (random) motion of the air molecules and we would have a perpetual buzz in our ears! The ear has a wide frequency response from about 15 or 20 Hz to about 20 kHz. Also, the ear has a large dynamic range; the ratio of the loudest sound pressure we can tolerate to the faintest we can hear is about 10 million (107). There are three essential reasons to consider the ear in this book. Sound pressure levels are now so high in industrialized societies that many individuals are exposed to intense noise and permanent damage results. Large numbers of other individuals are exposed to noise from aircraft, surface traffic, construction equipment or machines and appliances, and disturbance and annoyance results. Lastly there are subjective reasons. An understanding of people's subjective response to noise allows environmentalists and engineers to reduce noise in more effective ways. The human auditory response to sound concerns the science called psychoacoustics. For example, noise should be reduced in the frequency range in which the ear is most sensitive. Noise reduction should be by a magnitude which is subjectively significant. There are several other subjective parameters which are important in hearing.

Schematic illustration of the simplified cross-section through the human ear.

      4.2.1 Construction of the Ear

      The fleshy appendage on the side of the head (the pinna) is not as well developed in humans as in some animals. Its function is to focus sound into the ear canal. It helps us to localize the source of sound, particularly in the vertical direction, and is more effective at higher frequencies. The ear canal is about 25 mm long and ends at the tympanic membrane (eardrum) which is under tension and has the thickness of at sheet of paper.

Schematic illustration of tympanic membrane (eardrum) and three auditory ossicles. Schematic illustration of cochlea unwrapped to show working of the ear schematically.

      4.2.2 Working of the Ear Mechanism

      When a sound wave reaches the ear, it travels down the auditory canal until it reaches the eardrum. It sets the eardrum in motion and this vibration is transmitted across the 2 mm gap to the oval window by the lever system comprised of the auditory ossicles. It is thought that this mechanical system is an impedance matching device. The characteristic impedance, ρc, of air is approximately one two‐thousandth of the impedance of the cochlea fluid. The area of the tympanic membrane is 20 or 30 times larger than that of the oval window. Some believe that it is not the area of the oval window which is important, but rather the area of the footplate of the stapes. The tympanic membrane is about 20 times greater in area than the footplate area. However, not all of the tympanic membrane vibrates because it is firmly attached at its periphery. The ratio of the part of the tympanic membrane that moves to the footplate area is about 14 to 1.

      Also, the pivot of the ossicle system may be assumed closer to the oval window than the eardrum, hence providing a mechanical advantage of two or three times. The net result is that low‐pressure, high particle velocity amplitude air waves arriving at the eardrum are converted into high‐pressure low particle velocity amplitude fluid waves in the cochlea, approximately matching the air to fluid impedances. We probably remember from electrical theory that in order to obtain maximum power transfer, impedances must be matched.

      There is a “safety” device built into the inner ear mechanism. Attached to the malleus and stapes are two muscles: the tensor tympani and the stapedius. If continuous intense sounds are experienced, the muscles contract and rotate the ossicles so that the force passed onto the oval window does not increase correspondingly to the sound pressure.

      This effect is called the acoustic reflex and many types of experiments indicate that the reflex attenuates low‐frequency sound levels up to about 20 dB [9]. However, these muscles are rapidly fatigued by continuous narrow‐band intense noise. In addition, the muscles are relatively slow in their contraction making the reflex ineffective in presence of impulse or impact sounds. There seems to be some evidence that the muscles also contract when we speak, to prevent us hearing so much of our own speech.

      The Eustachian tube is used to equalize the pressure across the eardrum by swallowing. This explains why our ears “pop” in airplanes when we ascend and the atmospheric pressure changes. We may experience some pain in an airplane when landing again if we have a cold; mucus, blocking the Eustachian tube, can prevent us from equalizing the pressure by swallowing. Movement of the footplate

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