The warning tag on a lawn mower states that it produces noise at a level of 93 dB. What is this in watts per meter squared? 1= W/m²

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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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### Noise Level Conversion Exercise

**Question:** 

1. The warning tag on a lawn mower states that it produces noise at a level of 93 dB. What is this in watts per meter squared?

   \( I = \) [ Input Field ] \( \text{W/m}^2 \)

**Explanation:**

The task involves converting a sound level given in decibels (dB) to the corresponding intensity in watts per meter squared (\(\text{W/m}^2\)). 

#### Diagrams/Graphs:
There are no accompanying diagrams or graphs for this question. 

**Note for Educators:**
To solve this, students can use the formula that relates sound intensity levels in decibels to intensity in watts per meter squared:

\[ L = 10 \log \left( \frac{I}{I_0} \right) \]

Where:
- \( L \) is the sound level in dB
- \( I \) is the intensity in \(\text{W/m}^2\)
- \( I_0 \) is the reference intensity, \( 10^{-12} \, \text{W/m}^2 \)

Rearranging for \( I \):

\[ I = I_0 \times 10^{\frac{L}{10}} \]

Using the given \( L = 93 \, \text{dB} \):

\[ I = 10^{-12} \times 10^{\frac{93}{10}} \, \text{W/m}^2 \]

This calculation will yield the intensity in \(\text{W/m}^2\).
Transcribed Image Text:### Noise Level Conversion Exercise **Question:** 1. The warning tag on a lawn mower states that it produces noise at a level of 93 dB. What is this in watts per meter squared? \( I = \) [ Input Field ] \( \text{W/m}^2 \) **Explanation:** The task involves converting a sound level given in decibels (dB) to the corresponding intensity in watts per meter squared (\(\text{W/m}^2\)). #### Diagrams/Graphs: There are no accompanying diagrams or graphs for this question. **Note for Educators:** To solve this, students can use the formula that relates sound intensity levels in decibels to intensity in watts per meter squared: \[ L = 10 \log \left( \frac{I}{I_0} \right) \] Where: - \( L \) is the sound level in dB - \( I \) is the intensity in \(\text{W/m}^2\) - \( I_0 \) is the reference intensity, \( 10^{-12} \, \text{W/m}^2 \) Rearranging for \( I \): \[ I = I_0 \times 10^{\frac{L}{10}} \] Using the given \( L = 93 \, \text{dB} \): \[ I = 10^{-12} \times 10^{\frac{93}{10}} \, \text{W/m}^2 \] This calculation will yield the intensity in \(\text{W/m}^2\).
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