discussion symposium on hearing

DISCUSSION

SYMPOSIUM ON HEARING

BY F. W. KR^•z

Riverbank Laboratories, Geneva, Illinois

I believe that we all appreciate the importance of the sense of hearing in our daily life and appreciate the usefulness of the ear in the reception and interpretation of sounds. At least a part of the present discussion is concerned with an appreciation of the ear as a mechanism to serve certain purposes. There are two characteristics of the ear regarded as a physical instrument for sound reception and interpretation which are quite remarkable. One of these characteristics is, of course, the ability to analyze a sound into its component frequencies. The location of the analyzing mechanism or analyzing function has been the subject of much speculation and thought. As one may gather from having listened to the papers just given, most opinions have at least heretofore leaned toward a mechanical method of analysis, this mechanism being located in the inner ear and the results of this analysis being sent to the brain as separate components. In a discussion it is perhaps legitimate to point out in a general way what is involved and also some of the difficulties of this picture. The difficulties are quite apparent to those who have dealt with mechanical or electrical systems having natural periods covering such a wide range of frequencies as is covered by the human ear. This range is approximately from 20 vibrations per second to 20,000 vibrations per second, a matter of ten octaves. In terms of a piano key-board, the human hearing goes about one half an octave lower than the lowest note on a piano and something more than two octaves higher than the highest note on a piano. In a piano, the frequency of vibration of any one string is governed by three factors, the length of the string, the mass of the string per unit length, and the tension of the string. Those familiar with piano construction can readily appreciate the mechanical difficulties which would be encountered in extending the range of the piano by about three octaves. An extension of the range on the low frequency end would call for longer and heavier strings. An extension of the range on the high frequency end requires shorter strings with a higher tension than those now used. An extension of the range by three octaves would be a difficult mechanical problem and when this piano of extended range is imagined to be made in

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miniature so that it can be put into a case less than «'• in diameter, I believe that any mechanic would say that it was impossible. In the case of the basilar membrane of the ear, variations in the natural periods of the component parts are conceived of as being caused in part by the variations in loading or effective mass attached to the vibrating part by that part of the water of the inner ear which is moved by the vibration. The amount of water which acts to load a given part of the basilar membrane is considered as proportional to the path from the oval window to the membrane section and thence to the round window. This

would give a greater range than would be possible without the water loading but would still mean that all of the mechanical elements necessary for the complete range of tuned systems were contained within the same small volume before mentioned.

The accuracy of the adjustments, whatever they are and wherever they are, by which various frequencies are differentiated, is indicated by the very small change of pitch which can be readily and definitely detected, the detectable differences amounting to one quarter of one per cent change in pitch at some frequencies. This makes still more difficult the analogy of a piano mechanism and throws a still greater burden upon the mechanical design.

The permanence of adjustment of the frequency differentiation mechanism is another factor of vital importance in considering the probabilities of how the frequency analysis is accomplished. If we had but one ear, it would be rather difficult to show that the absolute adjustment is permanent, for it is possible that the whole scale of tuning could be shifted up or down and we might not be conscious of any change. We would, of course be conscious of any disturbance in the relative tuning of the elements such as might tend to cause an octave or other normal musical interval to be misjudged. However, we have two ears so that the check up of constancy of adjustment is always with us for while it is possible, nevertheless, it is highly improbable that a shift of tuning of the mechanism of the two ears would take place in such a fashion as to keep them alike.

So a mechanism which is to meet the requirements of sound analysis as well as our ears do, must have a frequency range of about ten octaves, must be very accurate in adjustment and must be essentially permanent in adjustment over a period of at least fifty years. This certainly seems rather difficult to achieve in the limited volume of the inner ear

and having as the sole materials of construction, the rather soft tissues which are found therein.


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1930] F. W. KRANZ 355

Another point which it seems may be commented on in considering the possibilities of mechanical tuned systems is the presence in some people of very abrupt changes in sensitivity, which are formed when the hearing is tested with a continuous tonal range. This abruptness makes difficult the concept of a frequency perception being due to a spread or region of the basilar membrane rather than a very narrowly restricted band and makes perhaps more difficult the idea that pitch perception is due to a vibration pattern of the basilar membrane. Changes in sensitivity are found which amount to changes of as much as 1000 in required energy for hearing with a change in pitch of a semitone.

I noted on one of Dr. Fletcher's slides which gave the possible selectivity which he calculated for the receptor system, that at 2000 cycles, where the selectivity is fairly good, there was a drop of one third of an octave on the low frequency side and two thirds of an octave on the high frequency side for a three bell drop in response, this being a ratio drop of 1000 in energy. This selectivity is not sufficient to account for the experimental facts.

The second characteristic of hearing which is quite remarkable from a purely mechanical standpoint, is its tolerance for a very wide range of intensities. The ratio of intensities between a painfully loud sound and a barely audible sound is approximately a million million to one. This means an amplitude ratio of the square root of this, or a million to one. This would be somewhat equivalent to a scale on which we could weigh a ton of coal and which would also be useable for weighing a mass of a few grams. Attempts have been made to explain this tolerance in terms of variation in nerve impulses sent to the brain from the ear but this explanation still leaves the burden of the million to one amplitude ratio in the inner ear. It is known that the muscles attached to the ossicles

of the middle ear exercise a very considerable restraining influence against excessively large vibrations which cuts down considerably the necessary ratio of amplitude for loud and weak sounds. In considering this problem of intensity tolerance with Dr. Pohlman, a further factor of some possible importance has seemed apparent. This is the difference in pressure exerted on the oval and round windows by an incoming sound. For weak sounds, the vibrations are transmitted to the oval window by means of the chain of ossicles without restraint from the ossicular muscles. For very intense sounds, this path of transmission is retarded by means of the ossicular muscles while at the same time the air vibration which is set up in the middle ear by the vibrations of the drum membrane impress themselves on the round window so that


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the round and oval windows are both affected by the incoming sound. These opposing forces tend to keep down the motion of the fluid in the inner ear and. so also the amplitude of the basilar membrane. I do not know whether or not this explanation has appeared in the literature but it seems that it is worthy of consideration.

It was perhaps due to lack of time that Dr. Fletcher did not explain the justification for cutting off about an octave and a half on each the high and low frequency ends of the frequency range in his consideration of frequency response. He considered a frequency range from 88 cycles to 8000 cycles instead of the known frequency range of 20 cycles to 20,000 cycles.

Dec. 13, 1929.


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discussion symposium on hearing

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