College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Y=1.5
![**Question:**
A sound of Y decibels has how much intensity in watts per square meter? (Show your calculations.) Is that enough to damage your hearing?
---
**Explanation:**
In order to determine the intensity of a sound in watts per square meter given a certain decibel level \( Y \), you can use the following formula:
\[ I = 10^{(L_dB - 120) / 10} \]
Where:
- \( I \) is the intensity in watts per square meter.
- \( L_dB \) is the sound level in decibels.
### Steps for Calculation:
1. **Convert the Decibel Level to Intensity:**
- Use the given decibel value \( Y \) in the formula above.
- Example: If \( Y = 80 \) decibels,
\[ I = 10^{(80 - 120) / 10} = 10^{-4} \]
\[ I = 0.0001 \, \text{W/m}^2 \]
2. **Assess the Potential for Hearing Damage:**
- Typically, intensities above 0.001 W/m² can be harmful with prolonged exposure.
- Note that the threshold for pain or immediate danger to hearing is around 1 W/m².
By performing these calculations, you can determine if the given sound intensity could potentially cause hearing damage based on scientific thresholds and guidelines for safe exposure levels.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f2aef95-130c-46da-800b-789dcb5b8580%2F7140207e-9f6e-42e4-b3cd-685f4e9d0ec1%2Fny6079_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A sound of Y decibels has how much intensity in watts per square meter? (Show your calculations.) Is that enough to damage your hearing?
---
**Explanation:**
In order to determine the intensity of a sound in watts per square meter given a certain decibel level \( Y \), you can use the following formula:
\[ I = 10^{(L_dB - 120) / 10} \]
Where:
- \( I \) is the intensity in watts per square meter.
- \( L_dB \) is the sound level in decibels.
### Steps for Calculation:
1. **Convert the Decibel Level to Intensity:**
- Use the given decibel value \( Y \) in the formula above.
- Example: If \( Y = 80 \) decibels,
\[ I = 10^{(80 - 120) / 10} = 10^{-4} \]
\[ I = 0.0001 \, \text{W/m}^2 \]
2. **Assess the Potential for Hearing Damage:**
- Typically, intensities above 0.001 W/m² can be harmful with prolonged exposure.
- Note that the threshold for pain or immediate danger to hearing is around 1 W/m².
By performing these calculations, you can determine if the given sound intensity could potentially cause hearing damage based on scientific thresholds and guidelines for safe exposure levels.
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