Question

The warning tag on a lawn mower states that it produces noise at a level of 91.0 dB. What is this in watts per meter squared?

Final Answer

$1.26 \times 10^{-3} \textrm{ W/m}^2$

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Video Transcript

This is College Physics Answers with Shaun Dychko.
We're told that a lawnmower has a noise level of 91 decibels, and we want to know what is the watts per meter squared. Well, we want to find the intensity, in other words. So, we know that the sound level is going to be ten times the logarithm of the intensity divided by this reference intensity, which is the threshold of hearing. So, we need to solve for

*I*. And we'll begin by dividing both sides by ten and we get this line here after switching the sides around as well to have the unknown on the left and then we'll raise both sides of this equation as exponents of ten. And so, ten to the power of logarithm base ten of*I*over*I naught*is*I*over*I naught*. And on the right hand side, we have ten to the power of sound level*B*divided by ten. And then multiply both sides by the reference intensity, and you get this line. So, intensity is reference intensity times ten to the power of the decibels divided by ten. So reference intensity is ten to the minus 12 watts per square meter. And multiply that by ten to the power of 91 decibels over ten, so that's basically ten to the power of 9.1. We end up with 1.26 times ten to the minus three watts per square meter.