Answer:
6.02dB
Explanation:
The sound level intensity can be calculated by using the formula:
[tex]I(dB)=10log_{10}(\frac{I}{I_o})[/tex]
where Io is the threshold of human hearing, and I is the intensity of the sound in at a certain distance. I is given by
[tex]I=\frac{P}{4\pi r^2}[/tex]
where P is the power of the source and r is the distance to the source. By replacing I in the expression for I(dB) we obtain
[tex]I(dB)=10log(\frac{P}{4\pi r^2I_o})=10log(\frac{P}{\pi r^2I_o})-10log(4)[/tex]
when jim halves the distance we have r'=1/2r:
[tex]I'(dB)=10log(\frac{P}{4\pi (\frac{1}{2}r)^2I_o})=10log(\frac{P}{\pi r^2I_o})[/tex]
Hence, the change o decibels is:
[tex]I'-I=10log(4)=6.02dB[/tex]
hope this helps!!
