A plane sound wave in a gas has pressure amplitude Δpₘ = 3 Pa, angular frequency 1000 rad/s, sound speed 300 m/s and equilibrium density ρ₀ = 1 kg/m³. If the particle-displacement amplitude is N μm, find N.
Physics · Wave Motion · sound wave
JEE Mains NEET JEE Advanced

Question

A plane sound wave in a gas has pressure amplitude Δpₘ = 3 Pa, angular frequency 1000 rad/s, sound speed 300 m/s and equilibrium density ρ₀ = 1 kg/m³. If the particle-displacement amplitude is N μm, find N.

Physics · Wave Motion · sound wave

G1 Physics · Accepted Answer

Use Δpₘ = ρ₀vωsₘ. Therefore, sₘ = Δpₘ/(ρ₀vω) = 3/[1×300×1000] = 10⁻⁵ m. Convert to micrometres: 10⁻⁵ m = 10 μm. Hence, N = 10.