Longitudinal waves are broadly used for the purposes of non-destructive evaluation of materials and for generation and sensing of acoustic vibration of surrounding medium by means of transducers. Many mathematical models describing longitudinal wave propagation in solids have been derived in order to analyse the effects of different materials and geometries on vibration characteristics without the need for costly experimental studies.
Reference:
Shatalov, M, Marais, J, Fedotov, I and Tenkam, MJ. Longitudinal vibration of isotropic solid rods: from classical to modern theories. Advances in Computer Science and Engineering. InTech
Shatalov, M., Marais, J., Fedotov, I., & Tenkam, M. (2011). Longitudinal vibration of isotropic solid rods: From classical to modern theories., Workflow;8300 InTech Open. http://hdl.handle.net/10204/5739
Shatalov, M, J Marais, I Fedotov, and MJ Tenkam. "Longitudinal vibration of isotropic solid rods: from classical to modern theories" In WORKFLOW;8300, n.p.: InTech Open. 2011. http://hdl.handle.net/10204/5739.
Shatalov M, Marais J, Fedotov I, Tenkam M. Longitudinal vibration of isotropic solid rods: from classical to modern theories.. Workflow;8300. [place unknown]: InTech Open; 2011. [cited yyyy month dd]. http://hdl.handle.net/10204/5739.