In the context of wave properties, which factor is inversely proportional to density and directly proportional to stiffness?

• A. Frequency
• B. Wavelength
• C. Speed
• D. Amplitude

Answer: (C)

The relationship between wave properties such as density, stiffness, speed, frequency, and wavelength is rooted in the fundamental physics of wave behavior in different media. In this case, speed refers to the speed of a wave traveling through a medium.

Specifically, speed is inversely proportional to the square root of density and directly proportional to the square root of stiffness. This relationship is often described by the wave speed equation:

[ v = \sqrt{\frac{E}{\rho}} ]

where (v) is the wave speed, (E) is the stiffness (or modulus of elasticity), and (\rho) is the density of the medium. As the density increases, the speed of the wave decreases, given that stiffness remains constant. Conversely, as stiffness increases, the speed of the wave increases, assuming density remains unchanged.

In the context of the options provided, speed is the only factor that exhibits this specific relationship of being inversely proportional to density while being directly proportional to stiffness. This illustrates the essential nature of how waves propagate through different materials and how their properties are influenced by the physical characteristics of the medium.