A small-amplitude plane sound wave propagates through a fluid with wave speed v. At a particular position and time the excess pressure is Δp and the corresponding excess density is Δρ. Which relation is correct?
Options

Question

A small-amplitude plane sound wave propagates through a fluid with wave speed v. At a particular position and time the excess pressure is Δp and the corresponding excess density is Δρ. Which relation is correct?

Options

G1 Physics · Accepted Answer

For small density variations, Δp = (B/ρ₀)Δρ. The speed of sound in the fluid is v² = B/ρ₀. Therefore, Δp = v²Δρ. Pressure variation and density variation are therefore in phase. Correct option: B.