Section 7.10 Loudness
Humans have a very wide range of hearing when measuring intensity in units of Watts per meter. For this reason, a logarithmic unit of measurement called sound intensity level is often used for measuring loudness. The unit for sound intensity level is the bel or decibel (dB).
Definition 7.10.1. Sound intensity level.
The intensity level of sound is defined to be:
\begin{equation*}
\beta = (10 \text{ dB}) \log_{10} \frac{I}{I_0}
\end{equation*}
\begin{equation*}
I_0 = 10^{-12} \frac{\text{W}}{\text{m}^2}
\end{equation*}
\(I_0\) is a very small intensity, at the lower limit of human hearing. When \(I = I_0\text{,}\) it dose not mean there are no sound waves present, just that humans cannot hear them.
When the sound intensity level increases by 10 dB, the intensity increases by a factor of ten. You start to feel pain from high intensity sound at about 130 dB
Exercises Activities
1. Explanation - Reference Intensity.
How loud is a noise that has an intensity of \(I = I_o\text{?}\)
2. Calculation - Whisper Intensity.
What is the intensity of a whisper (about 30 dB)? Include an explanation alongside your calculation.
