Question

The warning tag on a lawn mower states that it produces noise at a level of \(91.0\;{\rm{dB}}\). What is this in watts per meter squared?

Short answer

The intensity is \(1.3 \times {10^{ - 3}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).

Step-by-step solution

Given data

The intensity level is \(91.0\;{\rm{dB}}\).

The Sound intensity

The sound intensity results in loudness, which is the sound intensity ratio with the threshold. The intensity increases with the decrease in speed of sound in a medium.

Calculation of the intensity

Use the intensitylevel,

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

Substituting the values,

\(\begin{align}91.0 &= 10\log \frac{I}{{{{10}^{ - 12}}}}\\\frac{{91.0}}{{10}} &= \log \frac{I}{{{{10}^{ - 12}}}}\\{10^{9.1}} &= \frac{I}{{{{10}^{ - 12}}}}\\I &= {10^{9.1}} \times {10^{ - 12}}\\I &= 1.3 \times {10^{ - 3}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\end{align}\)

The noise in watts per meter squared is \(1.3 \times {10^{ - 3}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\)