Question

What intensity level does the sound in the preceding problem correspond to?

Short answer

The intensity level is \(84.5\;{\rm{dB}}\).

Step-by-step solution

Given Data

The intensity is \(I = 2.83 \times {10^{ - 4}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).

Sound intensity level

The intensity level is the logarithm of the sound intensity ratio to the threshold intensity—the unit of intensity level in dB.

Calculation of the intensity level

Use the intensity level of the sound as,

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

Substituting the values we get,

\(\begin{align}{\rm{dB}} &= 10\log \frac{{2.83 \times {{10}^{ - 4}}}}{{{{10}^{ - 12}}}}\\ &= 84.5\;{\rm{dB}}\end{align}\)

Therefore the levels of intensity is \(84.5\;{\rm{dB}}\)