Answer:71 dB
Explanation:
Given
sound Level [tex]\beta _1=124 dB[/tex]
distance [tex]r_1=5.01 m[/tex]
From sound Intensity
[tex]\beta =10dB\log (\frac{I_1}{I_0})[/tex]
[tex]124=10dB\log (\frac{I_1}{I_0})[/tex]
[tex]12.4=\log (\frac{I_1}{I_0})[/tex]
[tex]I_1=(1\times 10^{-12})\times 10^{12.4}[/tex]
[tex]I_1=2.51 W/m^2[/tex]
we know Intensity [tex]I\propto ^\frac{1}{r^2}[/tex]
[tex]I_1r_1^2=I_2r_2^2[/tex]
[tex]I_2=I_1(\frac{r_1}{r_2})^2[/tex]
[tex]I_2=2.51\cdot (\frac{5.01}{2.25\times 10^3})^2[/tex]
[tex]I_2=1.24\times 10^{-5} W/m^2[/tex]
Sound level corresponding to [tex]I_2[/tex]
[tex]\beta _2=10\log (\frac{I_2}{I_0})[/tex]
[tex]\beta _2=10\log (\frac{1.24\times 10^{-5}}{1\times 10^{-12}})[/tex]
[tex]\beta _2=70.93\approx 71 dB[/tex]