For a longitudinal sound wave with displacement s = s₀ cos(kx - ωt), the excess pressure is Δp = -β( $\delta$ s/ $\delta$ x) = βs₀k sin(kx - ωt). Which graph correctly represents Δp versus x?
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Question

For a longitudinal sound wave with displacement s = s₀ cos(kx - ωt), the excess pressure is Δp = -β( $\delta$ s/ $\delta$ x) = βs₀k sin(kx - ωt). Which graph correctly represents Δp versus x?

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G1 Physics · Accepted Answer

Step 1: For a longitudinal sound wave, Δp = -B(∂s/∂x). Thus pressure is π/2 out of phase with displacement in space. Step 2: Use the displacement slope/graph to determine compression, rarefaction and sign of Δp. Final: D: Image 4.

For a longitudinal sound wave with displacement s = s₀ cos(kx - ωt), the excess pressure is Δp = -β( δ \delta δ s/ δ \delta δ x) = βs₀k sin(kx - ωt). Which graph correctly represents Δp versus x?