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Sound Propagation in Elastic Materials

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In the previous pages, it was pointed out that sound waves propagate due to the vibrations or oscillatory motions of particles within a material. An ultrasonic wave may be visualized as an infinite number of oscillating masses or particles connected by means of elastic springs. Each individual particle is influenced by the motion of its nearest neighbor and both inertial and elastic restoring forces act upon each particle.

A mass on a spring has a single resonant frequency determined by its spring constant k and its mass m. The spring constant is the restoring force of a spring per unit of length. Within the elastic limit of any material, there is a linear relationship between the displacement of a particle and the force attempting to restore the particle to its equilibrium position. This linear dependency is described by Hooke's Law.

In terms of the spring model, Hooke's Law says that the restoring force due to a spring is proportional to the length that the spring is stretched, and acts in the opposite direction.Mathematically, Hooke's Lawis written as F =-kx, where F is the force, k is the spring constant, and x is the amount of particle displacement. Hooke's law is represented graphically it the right. Please note that the spring is applying a force to the particle that is equal and opposite to the force pulling down on the particle.


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