Question

A person standing 1.20 m from a portable speaker hears its sound at an intensity of 5.5x10^-3 W/m^2.

a) find the corresponding decibel level.

dB

b) Find the sound intensity (in W/m^2) at a distance of 36 m, assuming the sound propagates as spherical wave.

W/m^2

c) Find the decibel level at a distance of 36 m.

dB

Answer 1

(a) the expression to convert sound intensity to decibel level,

b = 10*log(I/Io)

b = 10* log (5.5*10^-3/10^-12)

b = 97.4 dB

(b) first we have to calculate the power emitted by the sound source,

P = I*A

P = 5.5*10^-3*4*π*1.2²

P = 99.52 * 10^-3 Watt

Now, intensity of the sound at 36 m,

I = P/A

I = 99.52 * 10^-3/(4*π*36²)

I = 6.11 * 10^-6 W/m²

(c) the expression to convert sound intensity to decibel level,

b = 10*log(I/Io)

b = 10* log (6.11*10^-6/10^-12)

b = 67.86 dB