What properties of material affect its speed of sound?

Of course, sound does travel at different speeds in different materials. This is because the mass of the atomic particles and the spring constants are different for different materials. The mass of the particles is related to the density of the material, and the spring constant is related to the elastic constants of a material. The general relationship between the speed of sound in a solid and its density and elastic constants is given by the following equation:

Where V is the speed of sound, C is the elastic constant, and p is the material density. This equation may take a number of different forms depending on the type of wave (longitudinal or shear) and which of the elastic constants that are used. The typical elastic constants of a materials include:

• Young's Modulus, E: a proportionality constant between uniaxial stress and strain.
• Poisson's Ratio, n: the ratio of radial strain to axial strain
• Bulk modulus, K: a measure of the incompressibility of a body subjected to hydrostatic pressure.
• Shear Modulus, G: also called rigidity, a measure of a substance's resistance to shear.
• Lame's Constants, l and m: material constants that are derived from Young's Modulus and Poisson's Ratio.

When calculating the velocity of a longitudinal wave, Young's Modulus and Poisson's Ratio are commonly used. When calculating the velocity of a shear wave, the shear modulus is used. It is often most convenient to make the calculations using Lame's Constants, which are derived from Young's Modulus and Poisson's Ratio.

It must also be mentioned that the subscript ij attached to C in the above equation is used to indicate the directionality of the elastic constants with respect to the wave type and direction of wave travel. In isotropic materials, the elastic constants are the same for all directions within the material. However, most materials are anisotropic and the elastic constants differ with each direction. For example, in a piece of rolled aluminum plate, the grains are elongated in one direction and compressed in the others and the elastic constants for the longitudinal direction are different than those for the transverse or short transverse directions.

Examples of approximate compressional sound velocities in materials are:

• Aluminum - 0.632 cm/microsecond
• 1020 steel - 0.589 cm/microsecond
• Cast iron - 0.480 cm/microsecond.

Examples of approximate shear sound velocities in materials are:

• Aluminum - 0.313 cm/microsecond
• 1020 steel - 0.324 cm/microsecond
• Cast iron - 0.240 cm/microsecond.

When comparing compressional and shear velocities, it can be noted that shear velocity is approximately one half that of compressional velocity. The sound velocities for a variety of materials can be found in the ultrasonic properties tables in the general resources section of this site.

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