Answer:
[tex]L = 96.2 dB[/tex]
Explanation:
As we know that the level of intensity is given as
[tex]\beta = 10Log(\frac{I}{I_o})[/tex]
here we know
[tex]\beta = 104 dB[/tex]
[tex]104 = 10Log(\frac{I}{10^{-12}})[/tex]
[tex]I = 0.025 W/m^2[/tex]
now the sound is travelling in all possible directions so we have
[tex]\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}[/tex]
[tex]\frac{0.025}{I_2} = \frac{10^2}{4.1^2}[/tex]
[tex]I_2 = 4.2 \times 10^{-3} W/m^2[/tex]
now for level of sound we have
[tex]L = 10Log(\frac{4.2 \times 10^{-3}}{10^{-12}})[/tex]
[tex]L = 96.2 dB[/tex]
