MadSci Network: Physics

Re: Will size of recipient affect the perception of pitch or tone?

Date: Sat Dec 20 21:12:32 2003
Posted By: Seth Horowitz, Faculty, Neuroscience, SUNY Stony Brook
Area of science: Physics
ID: 1071654471.Ph

Short answer: There are correlations between certain physical aspects of 
a sound (wavelength) and the physical size of auditory receptor organs, 
yielding differences in best frequency or ranges, but not quite the way 
you describe...  so...

The Long Answer: The modulation "height" of a sound is not measured in 
inches - amplitude modulation is measured in sound pressure level 
(usually expressed in decibels) so there is no physical dimensional 
correlate with the size of a listener.  A sound with a higher amplitude 
has the psychological corelate of being "louder."  However, there is a 
physical dimension which is critical to auditory perception - the 
wavelength of a sound which is the inverse of it's frequency.  And there 
are correlations between the size of a receiver and its auditory range 
and best frequencies.

Think about how a sound is generated for a moment (this may seem like a 
digression but I promise it's not).  Sound is generated when some surface 
(a string on an instrument, a membrane on a speaker, a fold of tissue in 
the larynx) vibrates at a specific rate.  If this vibration takes place 
in a medium in which sound can propagate (such as air or water), this 
vibration will travel through the medium at a specific velocity (the 
speed of sound - in air (at about room temperature at 50% humidity) will 
be about 344.62 m/sec (about 1131 feet per second).  If your sound source 
is vibrating at 1000 cycles per sec, that means it vibrates 1000 times 
every 344.62 meters or 1131 feet, so the wavelength of a 1000 Hz sound is 
about 1.1 feet long.  The wavelength of a sound at 100 Hz would be 11 
feet long and of a sound of 10,000 Hz would be 0.11 feet long. 

Here's where the correlation occurs between sound wavelength and a 
receiver's size comes in to play.  Sound is a mechanically coupled sense -
 it depends on a mechanical system to respond to the vibrational rate and 
amplitude of the incoming signal in such a way as to faithfully translate 
those signals into neural signals inside the ear.  While the stimulus 
seems simple, hearing mechanisms having undergone some pretty stunning 
evolutionary adaptations.  But all of them must transduce both the 
frequency (or it's inverse correlate, wavelength) and amplitude of a 
signal, whether you are dealing with a small underwater hagfish or a 
terrestrial elephant. Organisms hear across a variety of frequencies 
(their auditory range).  The range of detectable sound will vary based on 
a number of features, but mostly it is limited by the vibrational 
sensitivity or damping of their receiving organs.  (I am just going to 
discuss terrestrial vertebrates here, but invertebrates and aquatic 
organisms also have  wide array of hearing sensitivities, and many of the 
same principles apply, although the anatomy is often very very different 
due to the differences in the way sound propagates in air or water).  
Many amphibians and some reptiles hear through vibrations transmitted 
from their forelimbs to their shoulder girdles to their inner ear - this 
is called an opercularis pathway.  Amphibians (frogs in particular) who 
rely on this pathway have a strong correlation between frequency range 
and most sensitive frequency and the size of their body.  

Once you start dealing with organisms which have specific vibrational 
pathways for dealing with air-borne sounds, you have to start factoring 
in other stuctures rather than body size.  Amphibians with eardrums (such 
as modern ranid frogs such as the bullfrog) have a correlation between 
tympanic size and stiffness and most sensitive frequency and hearing 
range.  The reason for this is that if you have a receiver which is a 
vibratable membrane, a larger membrane will be able to respond to lower 
frequencies because it will have zones of lower stiffness - very small 
receivers tend to be very stiff and hence only respond to higher 
frequencies.  If you want to think of it in day to day application, think 
of your stereo speakers - the tweeters put out the highest frequencies 
and they are the smallest  The woofers or subwoofers put out the lowest 
frequencies and they are the largest.  Given a fixed power output, it is 
easy to move a small structures faster (higher frequency), whereas with 
the same power you can moved a larger structure slower (lower 

Once you get to an organism like mammals, you are dealing not only with 
eardrums, but a specialized membrane called the basilar membrane, which 
exists in the coiled cochlea or the inner ear.  If you unrolled this 
membrane, you'd find that the basal end, near the eardrum, is quite 
narrow and very stiff, whereas the apical end, furthest from the eardrum, 
is quite wide and not nearly as stiff.  Because of this, different 
regions of width and hence stiffness, will respond best to certain 
frequencies (or wavelengths).  To avoid getting into all the mechanics of 
neural auditory transduction, you can check out this very good overview 
page on basilar membrane function:

So there are correlates between a sound's wavelength and physical size 
(and hence stiffness) of parts of the receiver's auditory system.  So how 
does the physical size of the receiver factor in to this?  Well, in 
general a larger animal will have a larger vibrational receptive region 
than a smaller animal - a mouse hears well into the ultrasonic region 
(>20,000 Hz), whereas adult humans are pretty much limited to 20 Hz to 
18,000 Hz), and elephants actually use infrasonic (<20 Hz) for long 
distance communication.  There is a nice table showing differences in the 
audiograms of different animals here:

However; there are a lot of individual differences within a species - 
remember, although mechanical transduction is the basis of auditory 
input, processing is a neuroelectrical and neurochemical one, so there 
are a lot of factors which fine tune an individual's degree of auditory 
function.  And also bear in mind that although such a correlation can 
describe a best frequency or best auditory range, you do not just hear 
your most sensitive frequencies - punch enough power into an ultrasonic 
or infrasonic signal and even humans will hear it (although it's mostly 
very very irritating harmonics or subharmonics).

Believe it or not, that was a VERY short version of one part of the 
answer - I hope it clarified things...

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