Question

A person standing 1.05 m from a portable speaker hears its sound at an intensity of 6.30 x 10^-3 W/m²

a) Find the corresponding decibel level. (Answer in dB).

b) Find the sound intensity (in W/m² ) at a distance of 42.0 m, assuming the sound propagates as a spherical wave. ( answer in W/m² ).

c) Find the decibel level at a distance of 42.0 m. (answer in dB).

Answer 1

a)
L(dB) = 10 log(I/Io)
L(dB) = 10*log(6.30x10^-3 / 10^-12) = 98.0 dB

b)
I' = I / r^2
I' = 6.30x10^-3 / 42^2 = 3.6x10^-6 W/m^2

c)
L'(dB) = 10 log(I' / Io)
L'(dB) = 10*log(3.6x10^-6 / 10^-12) = 65.53 dB

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