A right-moving sound wave has particle displacement s = sₘ cos(kx-ωt). Let u be the instantaneous particle velocity and Δp the excess pressure at the same point. Which relation is correct?
Options

Question

A right-moving sound wave has particle displacement s = sₘ cos(kx−ωt). Let u be the instantaneous particle velocity and Δp the excess pressure at the same point. Which relation is correct?

G1 Physics · Accepted Answer

Particle velocity is u = ∂s/∂t = ωsₘ sin(kx−ωt). For the same wave, Δp = Bksₘ sin(kx−ωt). Using Bk = ρ₀v²(ω/v) = ρ₀vω, we get Δp = ρ₀vωsₘ sin(kx−ωt) = ρ₀vu. Thus pressure variation and particle velocity are in phase for a wave travelling along +x. Correct option: A.