A bird of approximately constant acoustic power flies directly towards a stationary listener by 30 m. During this motion the measured sound-intensity level rises by 12.04 dB. Neglect absorption and any Doppler-related change in radiated power. If the bird was initially N metres from the listener, find N.
Physics · Wave Motion · Beats, Loudness, Pitch and Characteristics of Sound
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Question

A bird of approximately constant acoustic power flies directly towards a stationary listener by 30 m. During this motion the measured sound-intensity level rises by 12.04 dB. Neglect absorption and any Doppler-related change in radiated power. If the bird was initially N metres from the listener, find N.

Physics · Wave Motion · Beats, Loudness, Pitch and Characteristics of Sound

G1 Physics · Accepted Answer

For a point source, I ∝ 1/r². A level increase of 12.04 dB gives 12.04 = 10log₁₀(I₂/I₁). Since 12.04 ≈ 10log₁₀16, I₂/I₁ = 16. Therefore, r₁²/r₂² = 16, so r₁/r₂ = 4. Also, r₁−r₂ = 30. Thus, 4r₂−r₂ = 30, 3r₂ = 30, r₂ = 10 m. Therefore, r₁ = 40 m. Hence, N = 40.