Assume that the displacement(s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement(s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f ). If Δp ~ 10 Pa, v ~ 300 m s⁻¹, ρ ~ 1 kg m⁻³ and f ~ 1000 Hz, then s will be the order of (Take multiplicative constant to be 1)
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Question

Assume that the displacement(s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement(s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f ). If Δp ~ 10 Pa, v ~ 300 m s⁻¹, ρ ~ 1 kg m⁻³ and f ~ 1000 Hz, then s will be the order of (Take multiplicative constant to be 1)

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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: B: (3/100) mm.