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# Relation of Sonic Velocity and Density

## Relation of Sonic Velocity and Density

(OP)
I am looking to calculate the density of a material, using an ultrasonic thickness gauge. Through physical measurement of the part I can use the gaue to obtain the sonic velosity of the material. However I am in need of the formula that relates the sonic velosity of the ceramic to the desity. If any of you are falmiliar with this relationship, I would appreciate the help!

Will

### RE: Relation of Sonic Velocity and Density

Sonic velocity is the speed of propagation of a pressure disturbance though a material. It is primarily a function of the translational and vibrational velocity of atoms a molecules since the disturbance prpogates from atom to atom. This is very dependent on temperature but not on density. If you campare a powdered material to its higher density solid form you will not find any difference in sonic velocity. The powder will absorb much more of the energy.

### RE: Relation of Sonic Velocity and Density

The longitudinal wave speed L in an elastic solid is equal to

L = (E/rho)^0.5

where E = Young's modulus and rho = mass density. Solving for the density,

rho = E/(L^2)

If you look up the modulus of elasticity, then you will be able to calculate the density of this material using the above equation. Good luck!

Maui

### RE: Relation of Sonic Velocity and Density

You need to know Young's Modulus.

### RE: Relation of Sonic Velocity and Density

(OP)
Thanks Maui,
That was exactly what I was looking for!!

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