Answer
a. $B \approx 75 dB$
b. $I \approx 3.16 * 10^{-3} \frac{W}{m^2}$
c. 102.009
Work Step by Step
Given the decibel equation $B = 10 \log \frac{I}{I_{0}}$
with $I_{0} = 10^{-12} \frac{W}{m^2}$
a. Given the intensity of the MP3 Sound at $I = 3.1 * 10^{-5} \frac{W}{m^2}$
Find the decibel level
$B = 10 \log \frac{3.1 * 10^{-5}}{10^{-12}}$
$B = 10 \log (3.1 * 10^7)$
$B \approx 75 dB$
b. Given the decibel level of a MP3 player with earbuds at $B = 95 dB$
Find the sound intensity
$95 = 10 \log \frac{I}{10^{-12}}$
$9.5 = \log \frac{I}{10^{-12}}$
$10^9.5 = \frac{I}{10^{-12}}$
$I = 10^{-2.5} \frac{W}{m^2}$
$I \approx 3.16 * 10^{-3} \frac{W}{m^2}$
c. Ratio of intensity with and without earbuds
$R = \frac{3.16 * 10^{-3}}{3.1 * 10^{-5}}$ = $102.009$
Thus the ratio is 102.009
