Firstly thank you very much for your answer, it helped me in building my knowledge about concrete rheology basics (experimentally and theoretically) and its evaluation.
Thus,
The formula: c = sqrt(Youngs Modulus/Density) is equivalent to the following formula:
YOUNG MODULUS: . The static Young's modulus is measured as specified by DIN 1048-5 by applying a load level of 1/3 of the compressive strength of the specimen. The "load level" caused by ultrasound waves is some decades lower. The corresponding modulus is defined as "dynamic Young's modulus".
Acoustic impedance really is Pressure/Acoustic Particle Velocity and equals rho*c for acoustic waves in gas.
Youngs Modulus = rho*c2, which is called the bulk modulus. This may perhaps be what you are after?
https://en.wikipedia.org/wiki/Bulk_modulus
Please note that a major difference, as compared to acoustics, is the fact that multiple wave types propagate in structures where only compression waves exist in gas. You have shear waves, bending waves, as well as some other wave types for structures.
What I am driving at is that you must make sure that you only base your determination of the wave speed c on compression waves as things otherwise go wrong.
In our lab, we're using P-waves (compressive uniaxial waves) in immersion testing (using immersion transducers).
Based on [Lester W, Schmerr Jr, in: Springer Nature, Fundamentals of Ultrasonic Nondestructive Evaluation - A Modeling Approach, Second Edition, Ames, Iowa, USA, 2016.]: The bulk modulus formula for a fluid can be used for an elastic solid (for example cement-based materials).
Based on [H. W. Reinhardt., C.U. Grosse., Continuous monitoring of setting and hardening of mortar and concrete, Construction and Building Materials 18 (2004) 145 – 154]: The formula that you already said is for the bulk modulus, is noted as Young's Modulus, and used in this article to evaluate Cement-Mortar behaviour.
If you need documentations (PDF files) for those two references, just share your personnal email.