Question

The sound intensity levels for a machine shop and a quiet library are 85 dB and 38 dB, respectively. What is the difference between the intensity of the sound in the machine shop and that in the library?

At a distance of 11.0 m from a point source, the intensity level is measured to be 75 dB. At what distance from the source will the intensity level be 37.5 dB?

Answer 1

Intensity of sound in the machine shop, Im  = Io * 10^(LI1/10)
Where Io is the threshold intensity, Io = 10^-12 W/m²

Im = 10^-12 * 10^(85/10)
Im = 0.00031622776 W/m^2

Intensity of sound in the Library, IL =  10^-12 * 10^(38/10)
IL = 6.309 * 10^-9 W/m^2

Difference btw the intensity, = 0.00031622776 - 6.309 * 10^-9
Difference btw the intensity, = 0.00031622145 W/m^2

Loss in Intensity = 75dB - 37.5dB = 37.5dB

dB = 10 * Log(p1/p0)
37.5 = 10 * Log(p1/p0)
(p1/p0) = 10^3.75 = 5623.4

If the distance increased by a factor of d, then the power increased by a factor of d^2:

5623.4 = d^2
d = 74.98

Distance from the source = 74.98 * 11.0 m = 824.8 m