Chapter 10: Q. 411 (page 1064)

What is the decibel level of a train whistle with intensity $10^{- 3}$ watts per square inch?

Short Answer

Expert verified

The decibel level of the train whistle is $90 d b$ .

Step by step solution

Step 1. Given and explanation

We know the intensity of the train whistle, i.e., $10^{- 3}$ .

We know that the loudness level, $D$ of sound of intensity, $I$ which is measured in watt per square inches is $D = 10 \log (\frac{I}{10^{- 12}})$ .

We also know that $(\frac{a^{m}}{a^{n}}) = a^{m} - a^{n}$ .

Applying these two formulas, we will calculate the decibel level.

Step 2. Substituting the value of I in the formula.

We have $D = 10 \log (\frac{I}{10^{- 12}})$ .

We know that $I = 10^{- 3}$ .

Substituting this,

$D = 10 \log (\frac{10^{- 3}}{10^{- 12}})$
Applying the formula $(\frac{a^{m}}{a^{n}}) = a^{m} - a^{n}$ , we get
localid="1645085584685" $D = 10 \log {(10)}^{- 3 + 12} D = 10 \log {(10)}^{9} D = 10 \cdot 9 \log (10) D = 90$
We know $\log_{10} (10) = 1$ , so we get the decibel level as $90 d b$ .

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What is the decibel level of a train whistle with intensity $10^{- 3}$ watts per square inch?

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Substituting the value of I in the formula.

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What is the decibel level of a train whistle with intensity 10-3watts per square inch?

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Substituting the value of I in the formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

What is the decibel level of a train whistle with intensity $10^{- 3}$ watts per square inch?