A plane sound wave has pressure amplitude Δpₘ = 20 Pa in a medium of density ρ₀ = 1.25 kg/m³ and sound speed v = 320 m/s. If its average intensity is N/2 W/m², find N.
Physics · Wave Motion · sound wave
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Question

A plane sound wave has pressure amplitude Δpₘ = 20 Pa in a medium of density ρ₀ = 1.25 kg/m³ and sound speed v = 320 m/s. If its average intensity is N/2 W/m², find N.

G1 Physics · Accepted Answer

Average intensity in terms of pressure amplitude is I = Δpₘ²/(2ρ₀v). Substitute: I = 20²/[2(1.25)(320)] = 400/800 = 0.5 W/m². Given I = N/2 W/m², N/2 = 1/2. Hence, N = 1.