From: e_p@unlinfo.unl.edu (edgar pearlstein)
Newsgroups: sci.physics
Subject: >Acoustics Problem for Swimmers: EXPLANATION
Date: 12 Dec 1992 19:21:25 GMT
Organization: University of Nebraska--Lincoln	
Distribution: world
NNTP-Posting-Host: unlinfo.unl.edu


A few days ago I posted the following:


>                    AN ACOUSTICS PROBLEM FOR SWIMMERS
>      When under water in a swimming pool one hears general noise - a 
> hissing sound, something like white noise.  I assume that this is due 
> to splashing and circulating water, as well as noise entering the water 
> from the air above.  A pool has very hard walls and bottom, so one 
> might expect a fairly uniform distribution of the sound. 
>      Now here's the problem:  I have noticed that when my head is only 
> a little below the surface, the hiss has a higher average pitch than 
> when it is farther down.  Why is this?
>      I think I know the answer, but I won't announce it yet.

       Here is the explanation that I favor:
            First consider standing waves within the water, in the ideal 
       case of nobody in the pool and the surface perfectly still.  The 
       wave pattern, for any frequency of sound that happens to be 
       present in the water, will have pressure ANTINODES at the bottom 
       and sides, but pressure NODES where the water meets air.  This 
       latter is because the speed of sound in water is much greater - 
       about a factor of 4.2 - than in air.  (Note that the ear responds 
       to pressure, not displacement.)  How deep does the node go?  
       Well, a quarter-wavelength below the surface there will be a 
       pressure ANTInode, for waves travelling perpendicular to the 
       surface. 
            Now let's put a swimmer in the water.  For sufficiently long 
       wavelengths, the pattern will be pretty much as described in the 
       paragraph above.  But for those frequencies whose wavelength is 
       smaller than, say, a few feet, the swimmer's body will greatly 
       change the standing wave pattern.  Also, ripples on the surface 
       will randomize things for wavelengths smaller than, say, four 
       times the ripple amplitude.  
            Thus we see that for high frequencies (short wavelength), 
       the standing wave pattern will be essentially random, while for 
       low frequencies there will be a pressure node close to the 
       surface.  So, since all frequencies are present in the noise,  
       the amount of high frequency sound perceived will be pretty much 
       independent of depth, while the amount of low frequency sound 
       will decrease as the ear gets close to the surface (pressure 
       antinode for low frequencies).  So the apparent pitch will rise 
       as the ear gets closer to the surface. 
            It remains to discuss what we mean by "high" and "low" 
       frequencies.  From the considerations of the second paragraph, it 
       appears that we mean wavelengths that are small and large 
       compared with a few feet.  In water, a wavelength of four feet 
       corresponds to a frequency of about 1200 Hz. 
                       ---------------------------------
            A few people suggested an explanation in terms of how one's 
       hearing is affected by the pressure of water, since as one goes 
       deeper, the pressure is greater.  For persons whose eustachian 
       tubes get blocked easily, there might be something to this, 
       although I doubt that it would explain the magnitude of the 
       effect.  
            For someone who has both the ambition and the equipment, I 
       can suggest an experiment to settle the question of whether the 
       effect is objective or subjective:  Use an underwater microphone, 
       connected to an amplifier and earphones above water.  Then listen 
       on the earphones as the mike's depth is varied.  To be fancier, 
       one could even Fourier analyze the signal from the mike. 

Edgar Pearlstein, University of Nebraska, Lincoln