Answer:
d) [tex]7.94\times 10^{9}[/tex]
Explanation:
β₁ = sound level of sound at rock concert = 120 dB
β₂ = sound level of sound due to whisper = 21 dB
I₁ = Intensity of sound at rock concert
I₂ = Intensity of sound due to whisper
sound level of sound at rock concert is given as
[tex]\beta _{1} = 10 log\left ( \frac{I_{1}}{10^{-12}} \right )[/tex]
[tex]120 = 10 log\left ( \frac{I_{1}}{10^{-12}} \right )[/tex]
[tex]12 = log\left ( \frac{I_{1}}{10^{-12}} \right )[/tex] Eq-1
sound level due to whisper is given as
[tex]\beta _{2} = 10 log\left ( \frac{I_{2}}{10^{-12}} \right )[/tex]
[tex]21 = 10 log\left ( \frac{I_{2}}{10^{-12}} \right )[/tex]
[tex]2.1 = log\left ( \frac{I_{2}}{10^{-12}} \right )[/tex] Eq-2
subtracting Eq-2 from Eq-1
[tex]12 - 2.1 = log\left ( \frac{I_{1}}{10^{-12}} \right ) - log\left ( \frac{I_{2}}{10^{-12}} \right )[/tex]
[tex]9.9 = log\left ( \frac{I_{1}}{I_{2}} \right )[/tex]
[tex]\left ( \frac{I_{1}}{I_{2}} \right ) = 7.94\times 10^{9}[/tex]
