Dear Oscar, sorry to see that your very interesting question has not yet been answered by experts in this field of research. As a synthetic inorganic chemist I would not call myself an expert enough to give you a qualified answer. However, I can recommend to you the following potentially useful literature references which hopefully help answering your question.:

High Pressure Thermoelasticity of Body-centered Cubic Tantalum

Article High Pressure Thermoelasticity of Body-centered Cubic Tantalum

This paper is freely accessible as public full text on RG.

For copper please see:

Atomistic shock Hugoniot simulation of single-crystal copper

Article Atomistic shock Hugoniot simulation of single-crystal copper

In this case you can easily request the full text of the paper directly from one of the authors via RG (four of them have RG profiles).

Some basic information can also be found in the respective Wikipedia entry at https://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements

Good luck with your work!

https://www.osti.gov/pages/servlets/purl/1421645

https://www.osti.gov/pages/servlets/purl/1421645,pls,kindly check this link

https://core.ac.uk/download/pdf/216304267.pdf,Also this link may be useful.

As respectful prof. Dr. Frank T. Edelemansaid,i would not call my self an expert enough to give a qualified answer&it’s far from my speciality,i recommended these links,may be useful with my respect.

Hi, Thank you all for your feedback. Unfortunately, it took a little time for me to reply as I'm on my Thanksgiving Break and have other pending duties on my house that I must take care of first.

I'm no longer working in the academic field. I can say that I'm Retired. Luckily, I found a good job and currently have good economic solvency to enjoy a few pleasures of life. I got the motivation to continue with this research as an old friend told me I should keep publishing, So hopefully if I finish this work, it may be helpful for someone out there. In the end, that's all it counts, Isn't it?

Best wishes

Dear Oscar Guerrero

Probably what you need to look at is for the experimental values of the elastic constants in the two metals: copper and tantalum:

Article Elastic Properties of Metals and Alloys. II. Copper

https://srd.nist.gov/jpcrdreprint/1.3253150.pdf

Do the same search for Tantalum.

Then if you know to which point group they belong, use the Christoffel equation to find the elastic speed for one longitudinal -L and two types of transversal waves -SV & -SH in those directions [100], [110] & [111], use an algebraic solver.

Cu, for example, has a cubic center point group but is said to be highly anisotropic so you need to consider anisotropy, which means, three different elastic velocities for Cu.

Article Elastic anisotropy of Cu and its impact on stress management...

Best Regards.

Thank you, Pedro L. Contreras E. , Faraed Salman and Frank T. Edelmann for the Feedback . I published on my Researchgate profile homepage a summary of this investigation. The link is below:Research My notes on the prediction of pressure induce phonon instabi...

Thank you so much, Prof. Oscar Guerrero

Muchas Gracias.