91Ó°ÊÓ

A sound's intensity in decibels (dB) is defined as \(d = 10 \log_{10} (\frac{I}{I_0})\), where \(d\) is the intensity level in decibels, \(I\) is the intensity of the sound, and \(I_0\) is the reference intensity. By setting \(d = 0\) and solving for \(I_0\), we find the reference intensity \(I_0\) as \(E_0\). To prove the intensity formula, we rearrange the decibel definition formula to isolate \(I\), divide both sides by 10, and apply the inverse property of logarithm to eliminate the logarithm. This results in the intensity formula \(I = E_0 10^{\frac{d}{10}}\), which shows that a sound with \(d\) decibels has an intensity of \(E_0 10^{d/10}\), where \(E_0\) is the intensity of a sound with 0 decibels.