Sound intensities, I, are often compared with the threshold of human hearing, I_0, which is about 10^-12 watts per meter squared. The relative intensity, R, of a sound is given by the equation: R = 10log(I/I_0)
i. The intensity of a whisper is about 300 times as loud as the threshold of human hearing. Find the relative intensity, R, of a whisper in decibels.
ii. Suppose a burglar alarm has a rating of 120 decibels. Compare this intensity to the threshold of human hearing.
+9673 The intensity of whisper is 300 times of the threshold. That means \(I_{\text{whisper}} = 300I_0\).
\(R_{\text{whisper}} = 10\log\left(\dfrac{300I_0}{I_0}\right) = 10\log 300 \approx 24.77\;\text{dB}\)
