(a) By what factor is one sound more intense than another if the sound has a level 17.0 dB higher than the other?

(b) If one sound has a level 32.0 dB less than another, what is the ratio of their intensities?

1 answer

(a)
L=10 log₁₀ (I₁/I₀)
ΔL= L₁ - L₂ =
=10 log₁₀(I₁/I₀) – 10log₁₀(I₂/I₀) =
=10 log₁₀(I₁/I₂)
ΔL/10 = log₁₀(I₁/I₂)
I₁/I₂ =10^( ΔL/10) =10^1.7 =50.1
(b)
I₁/I₂ =10^( ΔL/10) =10^3.2 =1584.8
I₂/I₁= 6.3•10⁻⁴
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