Question

You are standing 3.24 m from a loudspeaker and you detect an intensity level of 94.7 dB. At what distance from the loudspeaker would the intensity level be a more comfortable 77.1 dB? Assume the loudspeaker is an isotropic source. Answer in m

Answer 1

r₁ = 3.24 m

dB₁ = intensity level at distance 3.24 m , = 94.7 dB

dB₂ = intensity level at distance r₂ , = 77.1 dB

r₂ = ?

I₁ = Intensity at r₁ = ?

Using the equation

dB₁ = 10 log(I₁/10^-12)

dB₁ = 10 log(I₁/10^-12)

94.7 = 10 log(I₁/10^-12)

I₁ = 2.95 x 10^-3 W/m²

similarly

dB₂ = 10 log(I₂/10^-12)

77.1 = 10 log(I₂/10^-12)

I₂ = 5.13 x 10^-5 W/m²

we know that

I₁/I₂ = r₂²/r₁²

(2.95 x 10^-3)/(5.13 x 10^-5) = r₂²/(3.24)²

r₂ = 24.6 m