Question

Question: Ten cars in a circle at a boom box competition produce a \(120\;{\rm{dB}}\)sound intensity level at the center of the circle. What is the average sound intensity level produced there by each stereo, assuming interference effects can be neglected?

Short answer

The average sound intensity level is \(110\;{\rm{dB}}\)

Step-by-step solution

Sound intensity and Loudness

The sound intensity is the cause of loudness. The loudness is measured as the logarithm of the ratio of the intensity and the threshold intensity.

Calculation of the intensity

Use the intensity of the sound as,

\(d = 10\log \frac{I}{{{{10}^{ - 12}}}}\)

So,

\(\begin{align} 120 &= 10\log \frac{I}{{{{10}^{ - 12}}}}\\12 &= \log \frac{I}{{{{10}^{ - 12}}}}\\{10^{12}} &= \frac{I}{{{{10}^{ - 12}}}}\\I &= 1\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\end{align}\)

At the center of the circle, each car is responsible for one-tenth of the total intensity.

We can write,

\(\begin{align}d &= 10\log \frac{I}{{{{10}^{12}}}}\\ &= 10\log \frac{{0.1}}{{{{10}^{ - 12}}}}\\ &= 10 \times \log {10^{11}}\\ &= 110\;{\rm{dB}}\end{align}\)

Therefore average sound intensity level produced there by each stereo, assuming interference effects can be neglected is \(110\;{\rm{dB}}\).