At a distance of 5.20 m from a siren, the sound intensity is 4.07 x 102W/m?. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated. Number Units
At a distance of 5.20 m from a siren, the sound intensity is 4.07 x 102W/m?. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated. Number Units
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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![**Problem Statement:**
At a distance of 5.20 m from a siren, the sound intensity is \(4.07 \times 10^{-2} \, \text{W/m}^2\). Assuming that the siren radiates sound uniformly in all directions, find the total power radiated.
**Solution:**
To find the total power radiated by the siren, we can use the formula for sound intensity:
\[ I = \frac{P}{A} \]
where \( I \) is the sound intensity, \( P \) is the power, and \( A \) is the area over which the power is distributed. For a source radiating uniformly in all directions, the area \( A \) can be modeled as the surface area of a sphere:
\[ A = 4\pi r^2 \]
Given:
- Sound intensity \( I = 4.07 \times 10^{-2} \, \text{W/m}^2 \)
- Distance \( r = 5.20 \, \text{m} \)
Substitute the values into the equations to find the power \( P \):
\[ A = 4\pi (5.20)^2 \]
\[ P = I \times A \]
- Calculate \( A \).
- Multiply by \( I \) to find \( P \).
**Input Fields:**
- Number: [Input box for calculated power]
- Units: [Dropdown for selecting units, typically Watts (W)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F429a10f2-33bd-41fa-b013-8bbe810a9436%2Fab61ead8-094d-4585-a5ce-3988a89c1185%2Fbakzkg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
At a distance of 5.20 m from a siren, the sound intensity is \(4.07 \times 10^{-2} \, \text{W/m}^2\). Assuming that the siren radiates sound uniformly in all directions, find the total power radiated.
**Solution:**
To find the total power radiated by the siren, we can use the formula for sound intensity:
\[ I = \frac{P}{A} \]
where \( I \) is the sound intensity, \( P \) is the power, and \( A \) is the area over which the power is distributed. For a source radiating uniformly in all directions, the area \( A \) can be modeled as the surface area of a sphere:
\[ A = 4\pi r^2 \]
Given:
- Sound intensity \( I = 4.07 \times 10^{-2} \, \text{W/m}^2 \)
- Distance \( r = 5.20 \, \text{m} \)
Substitute the values into the equations to find the power \( P \):
\[ A = 4\pi (5.20)^2 \]
\[ P = I \times A \]
- Calculate \( A \).
- Multiply by \( I \) to find \( P \).
**Input Fields:**
- Number: [Input box for calculated power]
- Units: [Dropdown for selecting units, typically Watts (W)]
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