A small-amplitude sound wave has pressure amplitude Δpₘ = 10 Pa and wave speed v = 100 m/s. If the density-variation amplitude is Δρₘ = N×10⁻³ kg/m³, find N.
Physics · Wave Motion · sound wave
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Question

A small-amplitude sound wave has pressure amplitude Δpₘ = 10 Pa and wave speed v = 100 m/s. If the density-variation amplitude is Δρₘ = N×10⁻³ kg/m³, find N.

G1 Physics · Accepted Answer

For a sound wave, Δpₘ = v²Δρₘ. Therefore, Δρₘ = Δpₘ/v² = 10/100² = 10/10000 = 10⁻³ kg/m³. Hence, N = 1.