Answer:
The sound intensity of train is 1000 times greater than that of the library.
Explanation:
We have expression for sound intensity level,
[tex]L=10log_{10}\left ( \frac{I}{I_0}\right )[/tex]
A train whistle has a sound intensity level of 70 dB
We have
[tex]70=10log_{10}\left ( \frac{I_1}{I_0}\right )[/tex]
A library has a sound intensity level of about 40 dB
We also have
[tex]40=10log_{10}\left ( \frac{I_2}{I_0}\right )[/tex]
Dividing both equations
[tex]\frac{70}{40}=\frac{10log_{10}\left ( \frac{I_1}{I_0}\right )}{10log_{10}\left ( \frac{I_2}{I_0}\right )}\\\\\frac{7}{4}=\frac{log_{10}\left ( \frac{I_1}{I_0}\right )}{log_{10}\left ( \frac{I_2}{I_0}\right )}\\\\10^7\frac{I_2}{I_0}=10^4\frac{I_1}{I_0}\\\\\frac{I_1}{I_2}=10^3=1000[/tex]
The sound intensity of train is 1000 times greater than that of the library.
