Question

To quantify the intensity of sound, the decibel scale was developed. The formula for loudness L on the decibel scale is L=10logII0, where I0 is the intensity of sound just below the threshold of hearing, which is approximately 10−16 watt per square centimeter. Find the decibel reading for a sound with intensity 65,000 times I0.

Answer 1

`\begin{gathered} \text{Given:} \\ I_0=10^(-16)\text{ }W\/cm^2 \\ I=65000*10^(-16)\text{ }W\/cm^2\text{ (from the phrase 65,000 times }I_0) \\ L=10\log \mleft((I)/(I_0)\mright)\text{ the formula for loudness} \end{gathered}`

Substitute the following values to the given formula for loudness and we get

`\begin{gathered} L=10\log ((I)/(I_0)) \\ L=10\log (\frac{65000*10^(-16)\text{ }W\/cm^2}{10^(-16)\text{ }W\/cm^2}) \\ L=10\log (65000) \\ L=48.12913357dB \\ L=48dB\text{ (rounded off to nearest whole number)} \end{gathered}`

Therefore, the decibel reading is approximately 48 dB.