In a solid, the speed of sound is v = sqrt(K/ρ). What do K and ρ represent?

In a solid, the speed of sound is v = sqrt(K/ρ). What do K and ρ represent?

• A. K is the bulk modulus; ρ is the density
• B. K is kinetic energy; ρ is density
• C. K is bulk modulus; ρ is resistivity
• D. K is Young's modulus; ρ is density

Answer: (A)

The speed of a compression (longitudinal) wave in a solid comes from a balance between how stiff the material is against compression and how much mass has to move. The stiffness for uniform compression is captured by the bulk modulus, K. The inertia is set by the density, ρ (mass per unit volume). A larger K means the material resists compression more, so pressure disturbances propagate faster. A larger ρ means more mass to accelerate, which slows the wave. In the simple model for longitudinal waves in a uniform medium, this leads to v ≈ sqrt(K/ρ). So K represents the bulk modulus and ρ represents the density. The other options mix up the physical meanings (kinetic energy, resistivity, or Young’s modulus) and don’t fit this relationship.

The speed of a compression (longitudinal) wave in a solid comes from a balance between how stiff the material is against compression and how much mass has to move. The stiffness for uniform compression is captured by the bulk modulus, K. The inertia is set by the density, ρ (mass per unit volume). A larger K means the material resists compression more, so pressure disturbances propagate faster. A larger ρ means more mass to accelerate, which slows the wave. In the simple model for longitudinal waves in a uniform medium, this leads to v ≈ sqrt(K/ρ). So K represents the bulk modulus and ρ represents the density. The other options mix up the physical meanings (kinetic energy, resistivity, or Young’s modulus) and don’t fit this relationship.