1. ## Decibel work.

I got through 3 problems involving decibels, and now it asks me this: "How many times more intensity does a sound of 47dB have than a sound of 42dB?"
The decibel equation is: D = 10 log(I/10^-16) where I is intensity( $W/cm^2$) and D is decibels. And I might mention, intensity is in 10^-n and n is a number lower than 16

2. Hi

Let I1 be the intensity for D1 = 47 dB
Let I2 be the intensity for D2 = 42 dB

$D_1 = 10 \log \frac{I_1}{I_0}$

$D_2 = 10 \log \frac{I_2}{I_0}$

$D_1 - D_2 = 10 \log \frac{I_1}{I_0} - 10 \log \frac{I_2}{I_0}$

$D_1 - D_2 = 10 \,(\log \frac{I_1}{I_0} - \log \frac{I_2}{I_0})$

$D_1 - D_2 = 10 \,\log \frac{\frac{I_1}{I_0}} {\frac{I_2}{I_0}}$

$D_1 - D_2 = 10 \,\log \frac{I_1}{I_2}$

$\frac{I_1}{I_2} = 10^{\frac{D_1 - D_2}{10}}$