A right-moving sound wave has particle displacement s = sₘ cos(kx-ωt). Which statements are correct for the corresponding pressure and density variations?
Select all that apply

Question

A right-moving sound wave has particle displacement s = sₘ cos(kx−ωt). Which statements are correct for the corresponding pressure and density variations?

G1 Physics · Accepted Answer

For the given displacement wave, Δp = −B(∂s/∂x) = Bksₘ sin(kx−ωt). Also, Δp = v²Δρ, so pressure and density variations are in phase. Because displacement is proportional to cos(kx−ωt) while pressure is proportional to sin(kx−ωt), their phase difference is π/2. Maximum positive Δp corresponds to maximum compression. Therefore all four statements are correct.