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Re: [Phys-l] frequency and wavelength of sound in air



Yes, a standing wave can be established in a nearly-1D water channel; however, if you are referring to a surface wave (as at the air-water interface), the behavior is quite complicated (but understandable, and fascinating, to good undergraduates). The complications arise from the effects of the bottom of the channel (in the case of "shallow" water), and from dispersion in the wave equation (for all water depths). Incidentally, someone (perhaps Mr. Denker) mentioned solitons a few days ago; water surface waves are one of the systems where solitons are pretty easy to make (I used to make them in an irrigation trough when I was a kid, without really knowing what they were). The surface tension effects, dispersion, and gravity wave effects are nicely balanced for a wide range of parameters in this system, and various terms cancel each other out in interesting fashion.

The problem with suspending particles in water to observe standing waves (either at the surface, or within the water's bulk) is that radiation pressure from acoustic effects is usually pretty small, except at higher frequencies (it's difficult to get a ball thrown into a pond to move around based solely on throwing in rocks or sticks). Also, at some frequencies, particles of a given size and compressibility will gather at acoustic pressure nodes; at other frequencies or sizes or compressibilities, they'll gather at acoustic pressure antinodes. The frequencies and powers needed are usually quite high to get very noticeable effects (on the order of a MHz for a column a few inches long), so I'm not aware of an easy way of showing the effects under conditions which are very easily obtained by a home researcher.
For surface waves, you can sometimes show an effect with foam on top of the water (as in ponds, or in a coffee cup with a nice foam on the surface). In this case, things are complicated by the "Cheerio effect".

This is not an "visual" way of showing the lambda*f = const. relation, nor could you make quantitative measurements without an oscilloscope or at least perfect pitch, but it's at least somewhat indicative: Take a coffee cup of water, and heat it well in a microwave. Tap on the side with a spoon, to get a nice thunking tone. While doing so, pour in some instant coffee. What happens to the tone you hear? If you keep tapping, what will the tone eventually become?

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________________________________
From: ludwik kowalski <kowalskil@mail.montclair.edu>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Saturday, April 4, 2009 9:01:22 PM
Subject: Re: [Phys-l] frequency and wavelength of sound in air

On Apr 4, 2009, at 8:56 PM, Julie Quah wrote:

Just wondering, if the speed of sound in water is higher than that
in air,
Which of its, frequency or wavelength, (or both) increases in water?

A "gedanken demo" that comes to my mind is a standing wave in water
(or another liquid) with suspended particles. The known frequency is
changed and lambda is measured (observing suspended particles).

Can a one-dimensional standing wave be established in a narrow water
channel? If so then the (lambda*f=const) could be tested
experimentally for visible ways.

- - - - - - - - - - - - - -
Ludwik Kowalski, a retired physics teacher and an amateur journalist.
Updated links to publications and reviews are at:

http://csam.montclair.edu/~kowalski/cf/ http://csam.montclair.edu/~kowalski/my_opeds.html
http://csam.montclair.edu/~kowalski/revcom.html




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