medium's resistance to compression
Summary
This is the bulk modulus (B), the pressure change needed per fractional change in volume. A large B means the medium is hard to compress. The testable point is that sound speed is v = √(B/ρ), so stiffer media such as solids and liquids usually carry sound faster than gases.
Detail
Meaning: The bulk modulus B measures how much the pressure must change to produce a given fractional change in volume. A large B means a stiff medium that resists compression. Liquids and solids generally have much larger B than gases. A sound wave is a series of compressions and rarefactions, so B sets how strongly the medium pushes back, and a stiffer medium passes the disturbance along faster. Compressibility is the reciprocal, 1/B.
Equation: B = −V(ΔP/ΔV), and v = √(B/ρ). Here B is the bulk modulus (Pa), V is the original volume (m³), ΔP is the pressure change (Pa), ΔV is the volume change (m³), v is the speed of sound (m/s) and ρ is density (kg/m³). The minus sign makes B positive, because a pressure increase shrinks the volume.
On the MCAT: Passages compare the speed of sound in air, water and a solid and ask which is fastest. Other questions ask which material compresses most under the same pressure increase. You may calculate v from B and ρ, or use proportional reasoning: quadrupling B at fixed ρ doubles v. Some questions describe a fluid as incompressible, which treats B as very large.
Common confusion: Students see ρ in the denominator and conclude that denser media slow sound. B differs far more between gases and condensed phases than ρ does, so B usually dominates. Also, B describes resistance to uniform compression, not stretching (Young's modulus) or shearing (shear modulus).
Sources
- Physics (Cutnell and Johnson)
- Fundamentals of Physics (Halliday, Resnick and Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.