Question

What is the decibel level of one of the new quiet dishwashers with intensity ${10}^{-7}$watts per square inch?

Short answer

The decibel level of one of the new quiet dishwashers is$50db$.

Step-by-step solution

Step 1. Given information.

The given intensity is ${10}^{-7}$watts per square inch.

Here the loudness level, D, measured in decibels, of a sound of intensity, I, measured in watts per square inch is

localid="1645007369593" $D=10\log \left(\frac{I}{{10}^{-12}}\right)$.

Step 2. Finding the decibel level.

Here the intensity is ${10}^{-7}$watts per square inch then the decibel level is

$$\begin{gathered} D=10\log \left(\frac{{10}^{-7}}{{10}^{-12}}\right) \\ =10\log \left({10}^5\right) \\ =5\times 10 \\ =50 \end{gathered}$$

Therefore, the decibel level of one of the new quiet dishwashers is$50db$.