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- Path: sparky!uunet!think.com!ames!saimiri.primate.wisc.edu!crdgw1!newsun!dseeman
- From: dseeman@novell.com (Daniel Seeman)
- Newsgroups: sci.physics
- Subject: Re: >Acoustics Problem for Swimmers: EXPLANATION
- Message-ID: <1992Dec14.182239.5789@novell.com>
- Date: 14 Dec 92 18:22:39 GMT
- References: <1g2gi5INN3lb@crcnis1.unl.edu> <1gde3lINNfj5@crcnis1.unl.edu>
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-
- In article <1gde3lINNfj5@crcnis1.unl.edu> e_p@unlinfo.unl.edu (edgar pearlstein) writes:
- >
- >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.
-
- I understand your arguement and it seems to make sense. But if these standing
- waves and their ANTI-nodes are the explanation, then there must be other areas
- in the pool where only the higher frequencies can be heard. Or, does this mean
- the standing waves are shaped EXACTLY like the pool? Certainly for the case
- with only ONE node this may be the case. But what about
- higher order standing waves? There must be other areas in the pool where
- only the higher frequencies can be heard (not just areas near the surface...
- ). I say this because of the distribution of the nodes/ANTI-nodes in the
- 3-dimensional volume of the pool when considering higher order standing waves.
-
- Your microphone experiment would be able to map this out though. It sounds
- like a good senior project for someone. Try it out, write your paper and
- let us all know! This is a nice project!
-
- dks.
- > 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
- >
- >
- >
-