Intensity of Sound Wave (I = 2π²ν²a²ρv)

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I = 2π²ν²a²ρv

What each symbol means

SymbolWhat it stands for
IIntensity — energy transported per unit area per unit time (W/m²)
aAmplitude of wave (m)
vSpeed of sound in medium (m/s)
νFrequency of sound wave (Hz)
ρDensity of medium (kg/m³)

When to use this

I ∝ a² (intensity proportional to square of amplitude). I ∝ ν² (proportional to square of frequency). For a point source, I ∝ 1/r² (inverse square law). Can also write I = ½ρω²a²v using ω = 2πν. Loudness (in dB) = 10 log₁₀(I/I₀) where I₀ = 10⁻¹² W/m².