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young chul jung
young chul jung
01:41 Feb-08-1999
Dispersion curve vs Group velocity

hi, i am doing the ndt using Lamb waves on large concrete specimen for my master's thesis.
I am having a very hard time to understand what is the difference between dispersion relationship and group velocity.
I did some experiment and found out that whenever i do this testing. there are no similar result. i guess this problem is from Group velocity my teacher said.

i read a lot of papers and books to understand what the difference by phsically but i could not.

Could anyone explain me about this problem very easy way?
i got some reponse, but still very abstract.. and can not get like.." a ha.. that is it" something like that..

thanks a lot.

young

 Reply

Eric Sjerve
Eric Sjerve
02:03 Feb-24-1999
Re: Dispersion curve vs Group velocity
: hi, i am doing the ndt using Lamb waves on large concrete specimen for my master's thesis.
: I am having a very hard time to understand what is the difference between dispersion relationship and group velocity.
: I did some experiment and found out that whenever i do this testing. there are no similar result. i guess this problem is from Group velocity my teacher said.

: i read a lot of papers and books to understand what the difference by phsically but i could not.

: Could anyone explain me about this problem very easy way?
: i got some reponse, but still very abstract.. and can not get like.." a ha.. that is it" something like that..

: thanks a lot.

: young

When an ultrasonic pulse is sent into a medium, there will be a group of different wavelengths that make up the
pulse. This is due to the bandwidth of the crystal in the probe, which is in turn due to the pulse being
limited in time. These different wavelengths will normall travel at slightly different velocities, which leads
to pulse broadening as the ultrasonic pulse travels through the medium. The group velocity is the velocity of
the envelope of the pulse, and should under normal circumstances stay constant. A dispersion relationship
gives the dependance of the velocity on the wavelength, and will depend on the material through which the
ultrasonic pulse is traveling. Therefore, the dispersion relationship wil determine how much pulse broadening
occurs.

I hope this helps.

Eric.

 Reply

Rainer Meier
R & D
retired from intelligeNDT Systems & Services, Germany, Joined Nov 1998, 15

Rainer Meier

R & D
retired from intelligeNDT Systems & Services,
Germany,
Joined Nov 1998
15
00:47 Feb-26-1999
Re: Dispersion curve vs Group velocity
: : hi, i am doing the ndt using Lamb waves on large concrete specimen for my master's thesis.
: : I am having a very hard time to understand what is the difference between dispersion relationship and group velocity.
: : I did some experiment and found out that whenever i do this testing. there are no similar result. i guess this problem is from Group velocity my teacher said.

: : i read a lot of papers and books to understand what the difference by phsically but i could not.

: : Could anyone explain me about this problem very easy way?
: : i got some reponse, but still very abstract.. and can not get like.." a ha.. that is it" something like that..

: : thanks a lot.

: : young

: When an ultrasonic pulse is sent into a medium, there will be a group of different wavelengths that make up the
: pulse. This is due to the bandwidth of the crystal in the probe, which is in turn due to the pulse being
: limited in time. These different wavelengths will normall travel at slightly different velocities, which leads
: to pulse broadening as the ultrasonic pulse travels through the medium. The group velocity is the velocity of
: the envelope of the pulse, and should under normal circumstances stay constant. A dispersion relationship
: gives the dependance of the velocity on the wavelength, and will depend on the material through which the
: ultrasonic pulse is traveling. Therefore, the dispersion relationship wil determine how much pulse broadening
: occurs.

: I hope this helps.

: Eric.

I can't agree to "The bandwidth of the crystal". Even in the case of exciting only one discrete frequency,
you will get at least two different wave modes in a "thin plate", one asymetrical mode and one symetrical
mode (The higher the wall thickness times frequency - product, the more modes will be generated).
I'm not so familiar with the terms "group velocity" and "dispersion relationship", but I think, the group
velocity shouldn't be used in connection with dispersivephenomenons.

What I don't understand is the use of Lamb waves in large concrete specimen. Are this thin plates or beams?
How is the Thickness x Frequency - Product?
Can the different results of the tests be caused by material inhomogenities?

Rainer

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