Basic principles of ultrasonic primary responses in ultrasound-based detection techniques

Basic principles of ultrasonic primary responses in ultrasound-based detection techniques 

Most ultrasonic material analyses rely on measurements of some characteristic of ultrasonic waves propagating through the sample that provides information on the interaction of ultrasonic waves with the inside of the sample, thus enabling analysis of its physical and chemical properties. 

A plane ultrasonic wave can be described in terms of the displacement of a particle from its equilibrium position as a function of the distance the wave has travelled as follows  

In materials which are highly attenuating, the particle velocity and particle displacement are out of phase, so the elastic modulus and density of the material are complex and dynamic ( .e. frequency dependent). For many materials, the attenuation coefficient is fairly small ( .e. a co/c), so the particle velocity and displacement are in phase and Eq. 9.4 can be replaced with  

The speed of sound is directly proportional to the elastic moduli and inversely proportional to the density of the sample. 

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