If the distance between a point sound source and a dB detector is increased by a factor of 8,what will be the reduction in intensity level?
A)18 dB
B)0.016 dB
C)8 dB
D)65 dB
E)0.13 dB

Question

Quizplus · Accepted Answer

The intensity level in decibels (dB) is calculated using the formula $L = 10 \log \left(\frac{I}{I_0}\right)$, where $I$ is the intensity of the sound and $I_0$ is the reference intensity. The intensity of sound follows an inverse square law with distance, meaning if the distance is increased by a factor of 8, the intensity decreases by a factor of $8^2 = 64$. Using the formula for change in decibels, $\Delta L = 10 \log \left(\frac{1}{64}\right) = 10 \log \left(\frac{1}{2^6}\right) = 10 \times -6 \log(2) \approx -18 dB$, indicating an 18 dB reduction in intensity level.

If the Distance Between a Point Sound Source and a DB