Which property related to a medium's stiffness helps determine the propagation speed?

Which property related to a medium's stiffness helps determine the propagation speed?

• A. Bulk modulus
• B. Density
• C. Viscosity
• D. Temperature

Answer: (A)

The speed of a compressional wave in a medium is governed by how stiff the medium is compared with its inertia. The stiffness for resisting uniform compression is captured by the bulk modulus. A higher bulk modulus means the material resists compression more strongly, so pressure disturbances are transmitted more quickly, resulting in a faster propagation speed. In the typical relation c = sqrt(K/ρ) for fluids and gases, K is the bulk modulus and ρ is density; increasing K raises c, while increasing density lowers it because it adds inertia. Viscosity mainly affects damping and energy loss rather than the basic propagation speed, and temperature influences speed indirectly by changing density and modulus. So the bulk modulus is the best descriptor of stiffness that determines how fast the wave travels.

The speed of a compressional wave in a medium is governed by how stiff the medium is compared with its inertia. The stiffness for resisting uniform compression is captured by the bulk modulus. A higher bulk modulus means the material resists compression more strongly, so pressure disturbances are transmitted more quickly, resulting in a faster propagation speed. In the typical relation c = sqrt(K/ρ) for fluids and gases, K is the bulk modulus and ρ is density; increasing K raises c, while increasing density lowers it because it adds inertia. Viscosity mainly affects damping and energy loss rather than the basic propagation speed, and temperature influences speed indirectly by changing density and modulus. So the bulk modulus is the best descriptor of stiffness that determines how fast the wave travels.