Answer:
The sound intensity level at a distance of 1.0 km is 142 dB.
Explanation:
Given;
sound intensity level at 40 m = 170 dB
the sound intensity level of 170 dB in W/m²
[tex]dB = 10Log[\frac{I}{I_o} ]\\\\170 = 10Log[\frac{I}{I_o} ]\\\\17 = Log[\frac{I}{I_o} ]\\\\10^{17} = \frac{I}{I_o}\\\\I = 10^{17} \times \ I_o\\\\I = 10^{17} \times \ 10^{-12} \ W/m^2\\\\I = 10^{5} \ W/m^2[/tex]
To determine the sound at the second distance, apply the following equation of sound intensity.
[tex]I_1r_1^2 = I_2r_2^2\\\\I_2 = \frac{I_1r_1^2}{r_2^2} \\\\I_2 = \frac{(10^5)(40)^2}{(1000)^2}\\\\I_2 = 160 \ W/m^2[/tex]
The second intensity level is calculated as;
[tex]dB = 10Log[\frac{I_2}{I_o} ]\\\\dB = 10Log[\frac{160}{10^{-12}} ]\\\\dB = 142 \ dB[/tex]
Therefore, the sound intensity level at a distance of 1.0 km is 142 dB.
