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Re: [Phys-l] sound waves and beam flexures



I wondered about that also, but am more concerned at how to explain the difference between transverse wave in beams (rods) and ones in bulk seismic. From what I understand from reading the texts I have and the "web", seismic (not surface) waves both (approximately?) are described by the usual second order wave equation. The difference is in the appropriate modulus. (isotropic medium). But in a beam the transverse wave eq. includes a fourth order partial in the position. This necessarily results in dispersion. The usual solution(s) [functions of (ct-x)] , NOT. Instead phase speed is proportional to sqrt(omega) and also the attenuation. This means, for example, the shape of the initial pulse is not preserved.

I'm hunting around for a long Al rod to take measurements using the FFT app. included in LoggerPro and the microphone included w/ the LabQuest.

Here's a demo from Paul Doherty (Exploratorium) using a rod.

(no maths, but results from. Note the statement: the speed is a function of the rod diameter! I suspect as the diameter -> very large in the limit the speed will be the same as the seismic transverse one.)

http://www.exo.net/~Paul/summer_institute/summer_day11sound/ringing%20_Al_rod.html

bc

p.s. Note the direction WRT diameter is correct for my supposition.


On 2010, Feb 24, , at 08:31, Moses Fayngold wrote:



--- On Tue, 2/23/10, John Denker <jsd@av8n.com> wrote:


From: John Denker <jsd@av8n.com>
Subject: Re: [Phys-l] sound waves and beam flexures
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Date: Tuesday, February 23, 2010, 12:57 PM


And speaking of plane waves: for non-planar sound
waves, such as the spherical waves spreading out from
a point source, the physics is different. Specifically,
it is dispersive (whereas plane waves in the same medium
would be non-dispersive). "The wave equation" must be
reformulated to take this into account.


I do not see how and why the geometric shape of the wave-front can affect the dispersion. Whether a wave (more accurately, its propagation) is dispersive or not is determined by the properties of the medium and, if we also take into account the non-linear terms, by the wave amplitude, but not by geometry. In this respect I can understand that dispersion may be different for longitudinal and transverse wave since different elastic modulae of the medium would be involved in these two cases. But assuming the both waves are of the same kind (say, both longitudinal to make it more simple) AND neglecting the non-linear effects, the dispersion (as I understand it), must be the same for a plane and for a spherical wave.

Moses Fayngold,
NJIT



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