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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# 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?

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

See the step by step solution

## Step 1: Given data

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

## Step 2: 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.

## Step 2: Calculation of the intensity

Use the intensity level,

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

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 $$1.3 \times {10^{ - 3}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}$$