If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
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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![**Question 22:**
If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
**Solution Explanation:**
To calculate the noise level of 1000 flies, we first need to understand that sound levels in decibels (dB) are logarithmic, not linear.
The formula to add sound levels in decibels is derived from the logarithmic properties of sound, specifically:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( \sum_{i=1}^{n} 10^{L_i/10} \right) \]
Where \( L_{\text{total}} \) is the total sound level, and \( L_i \) is the sound level of each individual source.
Since all flies are identical and make the same noise level:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( 1000 \cdot 10^{40.0/10} \right) \]
Simplify:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( 1000 \times 10^4 \right) \]
\[ L_{\text{total}} = 10 \cdot \log_{10} (10^7) \]
\[ L_{\text{total}} = 10 \cdot 7 = 70 \, \text{dB} \]
Thus, the noise level of 1000 flies at that distance is 70 dB.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3998b89-6e6e-4832-8f26-2ad08d988cd1%2F4d172e7e-d3fe-4164-94b6-ed29f11a7f58%2Ftp9kl2_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 22:**
If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
**Solution Explanation:**
To calculate the noise level of 1000 flies, we first need to understand that sound levels in decibels (dB) are logarithmic, not linear.
The formula to add sound levels in decibels is derived from the logarithmic properties of sound, specifically:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( \sum_{i=1}^{n} 10^{L_i/10} \right) \]
Where \( L_{\text{total}} \) is the total sound level, and \( L_i \) is the sound level of each individual source.
Since all flies are identical and make the same noise level:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( 1000 \cdot 10^{40.0/10} \right) \]
Simplify:
\[ L_{\text{total}} = 10 \cdot \log_{10} \left( 1000 \times 10^4 \right) \]
\[ L_{\text{total}} = 10 \cdot \log_{10} (10^7) \]
\[ L_{\text{total}} = 10 \cdot 7 = 70 \, \text{dB} \]
Thus, the noise level of 1000 flies at that distance is 70 dB.
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