ARDMS Ultrasound Physics & Instrumentation Practice Exam

Which of the following statements about stiffness is incorrect?

1. Stiffness is directly related to propagation speed

2. Stiffness and density are related

3. Stiffness and propagation speed are indirectly associated

4. Stiffer mediums have faster propagation speeds

The correct answer is: Stiffness and propagation speed are indirectly associated

Stiffness is a crucial property of materials that influences how sound waves travel through them. Propagation speed in a medium is directly influenced by both stiffness and density, as described by the equation: \[ v = \sqrt{\frac{K}{\rho}} \] In this equation, \( v \) represents the propagation speed, \( K \) signifies the stiffness of the medium, and \( \rho \) denotes the density. From this relationship, it becomes clear that an increase in stiffness leads to an increase in propagation speed when density is held constant. Therefore, the statement about stiffness and propagation speed being indirectly associated is inaccurate. Instead, stiffness and propagation speed are directly associated—when stiffness increases, propagation speed also increases. In contrast, stiffness and density are related in that both influence the speed of sound in a material, leading to options indicating that stiffer mediums have faster propagation speeds and that stiffness is related to propagation speed being accurate. Recognizing the direct relationship between stiffness and propagation speed clarifies these concepts and their interconnections in ultrasound physics.