# Find the number of decibels for the power of the sound given. Round to the nearest decibel. A...

## Question:

Find the number of decibels for the power of the sound given. Round to the nearest decibel.

A rocket engine, {eq}2.50 \times {10^5}{\ \rm{ W}} \cdot {\rm{c}}{{\rm{m}}^2} {/eq} , what is the db?

## Finding the Number of Decibels:

The decibel formula can be used to find the number of decibels. The formula can be derived as, $$\begin{align} N=10\log \frac{P}{10^{-12 }}\ watts/m^{2}, \end{align} $$ where {eq}N {/eq} represents the number of decibels and {eq}P {/eq} represents the power output. Substitute the given values in the above formula to find the solution.

## Answer and Explanation:

Given:

{eq}P=2.50 \times {10^5} {/eq}

Now substitute the value in the formula, we get,

$$\begin{align} N=10\log \frac{2.50\times 10^{5}}{10^{-12}} \\ N=10\log\left [ 2.50\times 10^{17} \right ] \\ N=10\left [ \log\left ( 2.50+\log\left ( 10^{17} \right ) \right ) \right ] \\ N=10\left [ 0.3979+17 \right ] \\ N=10\left ( 17.4 \right ) \\ N=174dB \end{align} $$

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from Algebra I: High School

Chapter 8 / Lesson 13