Chapter 4.5, Problem 75PE

(a)

To determine

To calculate: The intensity at which the individual has a hearing impairment if the minimum intensity heard by an individual is $3.4\times {10}^{-8}{\text{W/m}}^2$. The formula $L=10\log \left(\frac{I}{I_0}\right)$ gives the loudness of sound L based on the intensity of sound I. The value $I_0={10}^{-12}{\text{W/m}}^2$ is the minimal threshold for hearing for mid frequency sounds. Hearing impairment is often measured according to the minimal sound level detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment.

$\begin{array}{cc}\text{Category}& \text{Loudness}\left(\text{dB}\right)\\ \text{Mild}& 26\le L\le 40\\ \text{Moderate }& 41\le L\le 55\\ \text{Moderately severe}& 56\le L\le 70\\ \text{Severe}& 71\le L\le 90\\ \text{Profound}& L>90\end{array}$

(b)

To determine

To calculate: The corresponding intensity of sound if the minimum loudness of sound detected by an individual is $30\text{ dB}$. The formula $L=10\log \left(\frac{I}{I_0}\right)$ gives the loudness of sound L based on the intensity of sound I. The value $I_0={10}^{-12}{\text{W/m}}^2$ is the minimal threshold for hearing for mid frequency sounds. Hearing impairment is often measured according to the minimal sound level detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment.

$\begin{array}{cc}\text{Category}& \text{Loudness}\left(\text{dB}\right)\\ \text{Mild}& 26\le L\le 40\\ \text{Moderate }& 41\le L\le 55\\ \text{Moderately severe}& 56\le L\le 70\\ \text{Severe}& 71\le L\le 90\\ \text{Profound}& L>90\end{array}$