Which expression correctly defines acoustic impedance?

Which expression correctly defines acoustic impedance?

• A. Density divided by speed
• B. Speed divided by density
• C. Density plus speed
• D. Density times speed

Answer: (D)

Acoustic impedance is the ratio of acoustic pressure to particle velocity for a wave. For a plane wave in a uniform medium, this impedance equals Z = ρ c, the product of density (ρ) and the speed of sound (c). This comes from the relationship p = ρ c u, where p is pressure and u is particle velocity, so Z = p/u = ρ c. That’s why the correct expression is density times speed. The other forms don’t match the units or the defined ratio: ρ/c, c/ρ, or ρ + c either have the wrong dimensions or mix incompatible quantities, while ρ c gives the correct unit in rayls (kg/(m^2·s)) and aligns with how impedance governs how strongly a medium resists sound and how reflections occur at boundaries.

Acoustic impedance is the ratio of acoustic pressure to particle velocity for a wave. For a plane wave in a uniform medium, this impedance equals Z = ρ c, the product of density (ρ) and the speed of sound (c). This comes from the relationship p = ρ c u, where p is pressure and u is particle velocity, so Z = p/u = ρ c. That’s why the correct expression is density times speed.

The other forms don’t match the units or the defined ratio: ρ/c, c/ρ, or ρ + c either have the wrong dimensions or mix incompatible quantities, while ρ c gives the correct unit in rayls (kg/(m^2·s)) and aligns with how impedance governs how strongly a medium resists sound and how reflections occur at boundaries.