A metal alloy as every solid propagates compressional waves that are "sound waves" with a sound speed of SQR(Young Modulus/Density) with an hysteretic damping generally close to 1E-3; measuring the Young Modulus is a simpler lab test than measuring the hysteretic damping, both can be made on a simple parallelepipedic sample; sound speed and sound absorption ((1-hysteretic damping)*number of wavelengthes) can be also assessed explicitly with an ultrasound probe on a rod (send a short pulse and compare with the echo).
If you manufacture a musical instrument and want to characterize the influence of the alloy on the musical quality of this instrument, this is an absolutely different issue calling for decades of research (the most popular is trying to understand the role of the varnish versus wood selection in Stradivarius violins): I would just ask a good musician to assess it by playing and ranking various instruments manufactured conventionally and by additive printing...
You probably want to investigate the resonant properties of the material and look into underlying principles such as Tribology (https://en.wikipedia.org/wiki/Tribology)