Answer:
The sound in a loud part of the room is 10000 times louder than sound in a quiet part of the same place.
Step-by-step explanation:
The acoustic intensity sound is a logarithmic function whose form is:
[tex]L = 10\cdot \log_{10}\left(\frac{I}{I_{o}} \right)[/tex]
Where:
[tex]L[/tex] - Acoustic intensity sound, measured in decibels.
[tex]I_{o}[/tex] - Reference sound intensity, measured in watts per square meter.
[tex]I[/tex] - Real sound intensity, measured in watts per square meter.
Sound intensity is now cleared:
[tex]10^{\frac{L}{10} } = \frac{I}{I_{o}}[/tex]
The ratio of the sound intensity in a loud part to the sound intensity in a quiet part is:
[tex]\frac{I_{100}}{I_{60}} = \frac{10^{\frac{100\,dB}{10} }}{10^{\frac{60\,dB}{10}}}[/tex]
[tex]\frac{I_{100}}{I_{60}} = \left(10^{100\,dB-60\,dB}\right)^{\frac{1}{10} }[/tex]
[tex]\frac{I_{100}}{I_{60}} = (10^{40\,dB})^{\frac{1}{10} }[/tex]
[tex]\frac{I_{100}}{I_{60}} =10^{4}[/tex]
The sound in a loud part of the room is 10000 times louder than sound in a quiet part of the same place.
